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E Math (IGCSE)

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IP Math

N(A) A Math

N(A) E Math

PSLE

PSLE Foundation Mathematics

<p>Expand and simplify</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$(4a-b+3)(4a-b-3)$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$(a+b+c)(a+b-c)$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$(3x-y)^2-(2x+y)^2+5x(y-x)$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$(2x+3)(3x+2)-6x(x+3)+5x+16$</span></div></li></ol>

Expanding and Simplifying Algebraic Products

IP1U4 SWI (Algebraic Identities) Q16

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">$(x-2y)(x^2-4y^2)(x+2y)$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$(x+2y-3z)^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$(a-2b+3c-1)(a+2b-3c-1)$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$(x-2y)(x+2y)-(x+2y)^2$</span></div></li></ol>

IP1U4 SWI (Algebraic Identities) Q15

<p>Expand and simplify</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$(a^2-1)^2-(a^2+1)^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$(s-2t)(-s-2t)-(s-2t)^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$(2a+3)^2+(3a-2)^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$(t-3)^2(t+3)^2(t^2+9)^2$</span></div></li></ol>

IP1U4 SWI (Algebraic Identities) Q14

<p>Expand and simplify</p>
<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">$\left( -\frac{1}{2}ab^2 - \frac{2}{3}c \right)^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$(-ab^2 - c)^2$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$(x - 3y)(3y - x)$</span></div></li><li><div class="list-item-content"><span class="list-item-text">$(a + b + c + d)^2$</span></div></li></ol>

$\left( -\frac{1}{2}ab^2 - \frac{2}{3}c \right)^2$

IP1U4 SWI (Algebraic Identities) Q13

<ol class="i-list"><li><div class="list-item-content"><span class="list-item-text">Expand and simplify $2(2x-3y)\left(\frac{1}{2x}-\frac{4}{3y}\right)$.</span><span class="inline-marks">[2]</span></div></li><li><div class="list-item-content"><span class="list-item-text">Expand and simplify $7y^2 - 4[3y^2 - 10y(2-y)]$.</span><span class="inline-marks">[2]</span></div></li></ol>

Expand and simplify $2(2x-3y)\left(\frac{1}{2x}-\frac{4}{3y}\right)$.

Expand and simplify $7y^2 - 4[3y^2 - 10y(2-y)]$.

IP1 Class Test (May 2025) Q9

<p>Expand and simplify each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Subtract $-p^3 + p^2 - p - 2$ from $5p^3 - 2p^2 + 2p - 10$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Subtract $2v^2 - 5$ from the sum of $3v^2 - 10v + 2$ and $1 - 5v - v^2$.</span></div></li><li><div class="list-item-paragraph">Subtract the product of ${8}$ and ${11-4m-m^{2}}$ from the product of ${-2}$ and ${m^{2}-3}$ .</div></li></ol>

Expand and simplify each of the following expressions.

Subtract $-p^3 + p^2 - p - 2$ from $5p^3 - 2p^2 + 2p - 10$.

Subtract $2v^2 - 5$ from the sum of $3v^2 - 10v + 2$ and $1 - 5v - v^2$.

Adding and Subtracting Polynomials

 Additions and Subtractions of Linear Algebraic Expressions

<p>Expand and simplify each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-content"><span class="list-item-text">Subtract $9x^3 - 2x^2 + 5x - 3$ from $6x^3 - x^2 + 10$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Subtract $y^2 - y + 3$ from the sum of $5y^2 + 10y - 2$ and $1- 5y - y^2$.</span></div></li><li><div class="list-item-content"><span class="list-item-text">Subtract the product of $2$ and $v^2 - 2v + 3$ from the product of $-4$ and $2 - v^2$.</span></div></li></ol>

Subtract $9x^3 - 2x^2 + 5x - 3$ from $6x^3 - x^2 + 10$.

Subtract $y^2 - y + 3$ from the sum of $5y^2 + 10y - 2$ and $1- 5y - y^2$.

Subtract the product of $2$ and $v^2 - 2v + 3$ from the product of $-4$ and $2 - v^2$.

 Expansion of Linear Algebraic Expressions

<p>If $P(x)=3{{x}^{3}}+11{{x}^{2}}-4x+5$and $Q(x)=x+7$, find </p>
<ol class="i-list"><li><div class="list-item-paragraph">$P(x)\times Q(x)$, </div></li><li><div class="list-item-paragraph">$P(2)\times Q(2)$, </div></li><li><div class="list-item-paragraph">the relationship between the degrees of $P(x),Q(x)$ and $P(x)\times Q(x)$.</div></li></ol>

If $P(x)=3{{x}^{3}}+11{{x}^{2}}-4x+5$and $Q(x)=x+7$, find 

Polynomial Notation, Degree and Evaluation

Multiplication of Polynomials

Polynomials, Cubic Equations and Partial Fractions

<p>Expand each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$-2\left( -5a+11 \right)$</div></li><li><div class="list-item-paragraph">$2\left( -3x+8y \right)$</div></li><li><div class="list-item-paragraph">$-3p\left( 4q-2r \right)$</div></li></ol>

Expand each of the following expressions.

Expansion of Linear Algebraic Expressions

Expansion of Linear Expressions

<p>Expand each of the following expressions.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$4(-2+b)$</div></li><li><div class="list-item-paragraph">$-3(x-5y)$</div></li><li><div class="list-item-paragraph">$-2m(3k-l)$</div></li></ol>

<p>Expand and simplify $\left( x+y \right)\left( 2a+b \right)-\left( x-2y \right)\left( 3b-a \right)$.</p>

Expand and simplify $\left( x+y \right)\left( 2a+b \right)-\left( x-2y \right)\left( 3b-a \right)$.

IP2U3 Exercise 1 Q14

Quadratic Functions, Equations and Inequalities

<p>Expand $\left( 2xy+3{{x}^{2}}+2 \right)\left( 5{{x}^{2}}y-1 \right)$.</p>

Expand $\left( 2xy+3{{x}^{2}}+2 \right)\left( 5{{x}^{2}}y-1 \right)$.

IP2U3 Exercise 1 Q13

<p>Expand and simplify $2{{x}^{3}}-y+\left( 2x+1 \right)\left( 3{{x}^{2}}-2x+1 \right)$.</p>

Expand and simplify $2{{x}^{3}}-y+\left( 2x+1 \right)\left( 3{{x}^{2}}-2x+1 \right)$.

IP2U3 Exercise 1 Q12

<p>Simplify $\left( x+6 \right)\left( 2y+3 \right)-\left( y+2 \right)\left( x-2 \right)$.</p>

Simplify $\left( x+6 \right)\left( 2y+3 \right)-\left( y+2 \right)\left( x-2 \right)$.

IP2U3 Exercise 1 Q11

<p>Expand and simplify $\left( -c-2d \right)\left( 2c-5d+3 \right)$.</p>

Expand and simplify $\left( -c-2d \right)\left( 2c-5d+3 \right)$.

IP2U3 Exercise 1 Q5

<p>Expand and simplify $2x\left( {{x}^{2}}-3y \right)$.</p>

Expand and simplify $2x\left( {{x}^{2}}-3y \right)$.

IP2U3 Exercise 1 Q3

<p>Expand and simplify $n\left( 2m-1 \right)-m\left( 3-n \right)$.</p>

Expand and simplify $n\left( 2m-1 \right)-m\left( 3-n \right)$.

IP2U3 Exercise 1 Q2

<p>Simplify ${5 \times a \times 4b - b \times a + 3a}$.</p>

Simplify ${5 \times a \times 4b - b \times a + 3a}$.

Addition and Subtraction of Linear Algebraic Expressions

1EM Unit 4 SW I Q2

<ol class="abc-list"><li><div class="list-item-paragraph">Expand and simplify $\left( a+3 \right)\left( a-2 \right)$.</div></li><li><div class="list-item-paragraph">Expand and simplify $\left( x-6y \right)\left( \frac{1}{x}+\frac{2}{3y} \right)$.</div></li></ol>

IP1U4 4.3 Worked Example 1

<p>Expand and simplify each of the following expressions completely.</p>
<ol class="abc-list"><li><div class="list-item-paragraph">$\left( \frac{x}{2}+\frac{4y}{3} \right)\left( \frac{4}{x}-\frac{y}{9} \right)$</div></li><li><div class="list-item-paragraph">$\left( \frac{1}{a}+\frac{1}{b} \right)\left( 3a-2b \right)$</div></li></ol>

Expand and simplify each of the following expressions completely.

Math Question Bank