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PSLE Foundation Mathematics

<p>Simplify the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">\((2x + 3y)^2\),</span></div></li><li><div class="list-item-paragraph">\((x + 2) - (2x - 4)(x - 3)\)</div></li></ol>

Expansion and Simplification of Quadratic Expressions

OPSS 2EM MYE 2018 Q6

Quadratic Functions, Equations and Inequalities

<p>Expand and simplify each of the following expressions.</p>
<ol class="i-list"><li><div class="list-item-paragraph">\({{\left( \frac{2x}{3}-\frac{1}{2} \right)}^{2}}\)<span class="inline-marks">[1]</span></div></li><li><div class="list-item-paragraph">\(\left( x+6 \right)\left( 2y+3 \right)-\left( y+2 \right)\left( x-2 \right)\)<span class="inline-marks">[2]</span></div></li></ol>

Expand and simplify each of the following expressions.

IP2 Class Test (May 2025) Q1

<p>Expand and simplify</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">\((-2m-3n)^2\)</span></div></li><li><div class="list-item-content"><span class="list-item-text">\((-2a+5b)^2\)</span></div></li><li><div class="list-item-content"><span class="list-item-text">\((4m+n)^2\)</span></div></li><li><div class="list-item-content"><span class="list-item-text">\((-3a-2b)^2\)</span></div></li></ol>

IP1U4 SWI (Algebraic Identities) Q4

Algebraic Expressions, Identities and Formulae

<p>Expand and simplify</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">\((y+8)^2\)</span></div></li><li><div class="list-item-content"><span class="list-item-text">\((t+6)^2\)</span></div></li><li><div class="list-item-content"><span class="list-item-text">\((a+2b)^2\)</span></div></li><li><div class="list-item-content"><span class="list-item-text">\((3a-5)^2\)</span></div></li></ol>

IP1U4 SWI (Algebraic Identities) Q3

<p>Expand and simplify</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">\((2x+1)(2x-1)\)</span></div></li><li><div class="list-item-content"><span class="list-item-text">\((3m+4)(3m-4)\)</span></div></li><li><div class="list-item-content"><span class="list-item-text">\((3y+5)(3y-5)\)</span></div></li><li><div class="list-item-content"><span class="list-item-text">\((2t+7)(2t-7)\)</span></div></li></ol>

IP1U4 SWI (Algebraic Identities) Q2

<p>Expand and simplify</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">\((x+2)(x-2)\)</span></div></li><li><div class="list-item-content"><span class="list-item-text">\((y+5)(y-5)\)</span></div></li><li><div class="list-item-content"><span class="list-item-text">\((y-6)(y+6)\)</span></div></li><li><div class="list-item-content"><span class="list-item-text">\((x+7)(x-7)\)</span></div></li></ol>

IP1U4 SWI (Algebraic Identities) Q1

<ol class="abc-list"><li><div class="list-item-paragraph">Expand \(\left( 2x-3 \right)\left( 2x+3 \right)\).</div></li><li><div class="list-item-paragraph">Hence, find the value of \(397\times 403\) without the use of a calculator. Show your workings clearly.</div></li></ol>

Evaluating Expressions using Special Identities

Expansion and Application of Special Products

<ol class="abc-list"><li><div class="list-item-paragraph">Expand and simplify \({{\left( 3a+3b \right)}^{2}}\).</div></li><li><div class="list-item-paragraph">If&nbsp;\({{a}^{2}}+{{b}^{2}}=61\) and \(ab=30\), find the value of \({{\left( 3a+3b \right)}^{2}}\).</div></li></ol>

Application of Perfect Square Identities

<p>Expand each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">\({{\left( x+7 \right)}^{2}}\)</div></li><li><div class="list-item-paragraph">\({{\left( 3x+5y \right)}^{2}}\)</div></li><li><div class="list-item-paragraph">\({{\left( 9-x \right)}^{2}}\)</div></li><li><div class="list-item-paragraph">\({{\left( 3x-8y \right)}^{2}}\)</div></li><li><div class="list-item-paragraph">\(\left( x-10 \right)\left( x+10 \right)\)</div></li><li><div class="list-item-paragraph">\(\left( 2x-7y \right)\left( 2x+7y \right)\)</div></li></ol>

Expand each of the following expressions.

Expanding Expressions Using Standard Identities

<div class="content-block content-block--table"><div class="table-container"><table style="table-layout: fixed; width: 200px;"><colgroup><col style="width: 200px;"></colgroup><thead><tr><th style="text-align: left; --cell-justify: flex-start"><div style="text-align: center;">     <p>\({(a + b)^2 = a^2 + 2ab + b^2}\)</p>     <p>\({(a - b)^2 = a^2 - 2ab + b^2}\)</p>     <p>\({(a + b)(a - b) = a^2 - b^2}\)</p>   </div></th></tr></thead><tbody></tbody></table></div></div>
<p>Expand each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">\({{\left( x+4 \right)}^{2}}\)</div></li><li><div class="list-item-paragraph">\({{\left( 3x+8 \right)}^{2}}\)</div></li><li><div class="list-item-paragraph">\({{\left( 7-x \right)}^{2}}\)</div></li><li><div class="list-item-paragraph">\({{\left( 3x-4y \right)}^{2}}\)</div></li><li><div class="list-item-paragraph">\(\left( x-3 \right)\left( x+3 \right)\)</div></li><li><div class="list-item-paragraph">\(\left( 3x-4y \right)\left( 3x+4y \right)\)</div></li></ol>

Applying Special Algebraic Formulae

<p>Expand and simplify each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">\(\left( x+8y \right)\left( 2x-y \right)\)</div></li><li><div class="list-item-paragraph">\(\left( {{x}^{2}}-4 \right)\left( 7x-8 \right)\)</div></li><li><div class="list-item-paragraph">\(\left( 2x-y \right)\left( 3x-4y \right)-\left( 2x-y \right)\left( x+4y \right)\)</div></li><li><div class="list-item-paragraph">\(\left( x-6y \right)\left( x+5y-2 \right)\)</div></li><li><div class="list-item-paragraph">\(\left( x+4 \right)\left( {{x}^{2}}-8x-5 \right)\)</div></li></ol>

Polynomial Expansion and Simplification

<p>Expand and simplify each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">\(\left( 2x-3y \right)\left( 2x+6y \right)\)</div></li><li><div class="list-item-paragraph">\(\left( 3{{x}^{2}}-2 \right)\left( 6x-4 \right)\)</div></li><li><div class="list-item-paragraph">\(\left( x-3y \right)\left( 3x+2y \right)-\left( 5x+2y \right)\left( 4x-3y \right)\)</div></li><li><div class="list-item-paragraph">\(\left( 2x-y \right)\left( 4x+3y+2 \right)\)</div></li><li><div class="list-item-paragraph">\(\left( 6x-5 \right)\left( 3{{x}^{2}}+4x+3 \right)\)</div></li></ol>

Expanding Products of Binomials and Polynomials

<p>Expand and simplify each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">\(9x\times \left( -2y \right)\)</div></li><li><div class="list-item-paragraph">\(2x{{y}^{3}}\times 6x{{y}^{2}}\)</div></li><li><div class="list-item-paragraph">\(x\left( 5y+9 \right)\)</div></li><li><div class="list-item-paragraph">\(-4x\left( -x+3y \right)\)</div></li><li><div class="list-item-paragraph">\(3z\left( 6x+y \right)+8z\left( x-5y \right)\)</div></li><li><div class="list-item-paragraph">\(-x\left( 5y+2z \right)-7x\left( y-4z \right)\)</div></li></ol>

Algebraic Expansion with Variables

<p>Expand and simplify each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">\(5x\times \left( -8y \right)\)</div></li><li><div class="list-item-paragraph">\(3x{{y}^{2}}\times 4x{{y}^{2}}\)</div></li><li><div class="list-item-paragraph">\(x\left( 2y+3 \right)\)</div></li><li><div class="list-item-paragraph">\(-2x\left( 5x-3y \right)\)</div></li><li><div class="list-item-paragraph">\(4z\left( 5x+y \right)+7z\left( x-3y \right)\)</div></li><li><div class="list-item-paragraph">\(-3x\left( 2y+z \right)-2x\left( 4y-6z \right)\)</div></li></ol>

Algebraic Expansion with Multiple Variables

<p>Expand and simplify each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">\(\left( x+7 \right)\left( x+8 \right)\)</div></li><li><div class="list-item-paragraph">\(\left( 3x-7 \right)\left( 5x-8 \right)\)</div></li><li><div class="list-item-paragraph">\(\left( 9+4x \right)\left( x-11 \right)\)</div></li><li><div class="list-item-paragraph">\(\left( 5-11x \right)\left( 7x-2 \right)\)</div></li><li><div class="list-item-paragraph">\(\left( x-2 \right)\left( 3x+5 \right)-5x\left( x-7 \right)\)</div></li></ol>

Expansion and Simplification of Algebraic Expressions

<p>Expand and simplify each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">\(\left( x+3 \right)\left( x+5 \right)\)</div></li><li><div class="list-item-paragraph">\(\left( 4x-5 \right)\left( 6x-7 \right)\)</div></li><li><div class="list-item-paragraph">\(\left( 6+2x \right)\left( 3-4x \right)\)</div></li><li><div class="list-item-paragraph">\(\left( 2-8x \right)\left( 13x-5 \right)\)</div></li><li><div class="list-item-paragraph">\(\left( x+6 \right)\left( x-5 \right)-\left( x+3 \right)\left( x-2 \right)\)  </div></li></ol>

Expanding Algebraic Expressions Using the Distributive Property

<p>Expand and simplify each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">\(3a\left( 6+a \right)-2\left( 5a-4 \right)\)</div></li><li><div class="list-item-paragraph">\(-x\left( 9-3x \right)+5x\left( x-9 \right)\)</div></li><li><div class="list-item-paragraph">\(2{{x}^{2}}+3x-8-\left( -12{{x}^{2}} \right)-6x-2\)</div></li><li><div class="list-item-paragraph">\(x+\left( -3{{x}^{2}} \right)+3\left( 4{{x}^{2}}-7x \right)\)</div></li><li><div class="list-item-paragraph">\(2\left( 2-8{{x}^{2}}-9x \right)-5\left( {{x}^{2}}-3x-6 \right)\)</div></li></ol>

Expanding and Simplifying Algebraic Expressions

<p>Expand and simplify each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">\(x\left( 3x+2 \right)+4x\left( x-4 \right)\)</div></li><li><div class="list-item-paragraph">\(6\left( x-5 \right)-4\left( 3x+5 \right)\)</div></li><li><div class="list-item-paragraph">\(5{{x}^{2}}-2-\left( 8{{x}^{2}}+14x-3 \right)\)</div></li><li><div class="list-item-paragraph">\(3\left( {{x}^{2}}+5x-6 \right)-\left( 7+2{{x}^{2}} \right)\)</div></li></ol>

Expanding and Simplifying Quadratic Expressions

<p>Simplify the following expressions. </p>
<ol class="abc-list"><li><div class="list-item-paragraph">\(8{{x}^{2}}+2x-4{{x}^{2}}+19-5x\)</div></li><li><div class="list-item-paragraph">\(16{{x}^{2}}-22-28{{x}^{2}}-2+3x\) </div></li></ol>

Simplifying Quadratic and Linear Terms

<p style="margin-left: 0.5rem">Tips:</p>
<p>•	Add or subtract only the like terms. </p>
<p>•	When adding or subtracting like terms, we simply add or subtract the coefficients. </p>
<ol class="abc-list"><li><div class="list-item-paragraph">\(3{{x}^{2}}-2+{{x}^{2}}+x+1\)</div></li><li><div class="list-item-paragraph">\(7{{x}^{2}}+19+8{{x}^{2}}-2\)</div></li></ol>

•	Add or subtract only the like terms. 

•	When adding or subtracting like terms, we simply add or subtract the coefficients. 

Math Question Bank