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PSLE Foundation Mathematics

Simplify $[(a+b)^2 - (a-b)^2] \div 4ab$

Simplify $[(a+b)^2 - (a-b)^2] \div 4ab$

Simplifying Algebraic Fractions involving Factorisation

IP1U4 SWII (Further App. of Alg. Id.) Q6

Algebraic Expressions, Identities and Formulae

<ol class="i-list"><li><div class="list-item-paragraph">Simplify the following expression:</div><div class="list-item-paragraph" style="text-align: center"> $\frac{a^2 + b^2 + 2ab}{a^2 - b^2}$</div></li><li><div class="list-item-paragraph">Hence evaluate $\frac{55^2 + 45^2 + 2 \times 55 \times 45}{55^2 - 45^2}$</div></li></ol>

Hence evaluate \[\frac{55^2 + 45^2 + 2 \times 55 \times 45}{55^2 - 45^2}\]

Evaluating Expressions using Special Identities

IP1U4 SWII (Further App. of Alg. Id.) Q5

Quadratic Functions, Equations and Inequalities

Simplify $\frac{2{{a}^{2}}-12a+18}{{{a}^{2}}-6a-ab+3b+9}$.

Simplify $\frac{2{{a}^{2}}-12a+18}{{{a}^{2}}-6a-ab+3b+9}$.

Factorising Polynomials to Reduce a Rational Expression

Simplify $\frac{{{x}^{2}}+x-2xy-2y}{{{x}^{2}}-4xy+4{{y}^{2}}}$.

Simplify $\frac{{{x}^{2}}+x-2xy-2y}{{{x}^{2}}-4xy+4{{y}^{2}}}$.

Factorising Polynomials in Two Variables

Simplify $\frac{2xw+2wy-x-y}{4w-2}$.

Simplifying Algebraic Fractions (Factorisation)

Simplify $\frac{{{x}^{2}}-16{{y}^{2}}}{{{x}^{2}}+10xy+24{{y}^{2}}}$.

Simplify $\frac{{{x}^{2}}-16{{y}^{2}}}{{{x}^{2}}+10xy+24{{y}^{2}}}$.

Simplifying Rational Expressions with Two Variables

Simplify $\frac{9-{{x}^{2}}}{9-6x+{{x}^{2}}}$ .

Simplify $\frac{9-{{x}^{2}}}{9-6x+{{x}^{2}}}$ .



Simplifying Rational Expressions (Difference of Squares)

Simplify $\frac{{{x}^{2}}+2x-8}{{{x}^{2}}-7x+10}$.

Simplify $\frac{{{x}^{2}}+2x-8}{{{x}^{2}}-7x+10}$.

Simplifying Rational Expressions (Quadratic Forms)

Simplify $\frac{5p+10{{p}^{2}}}{10+20p-5q-10pq}$.

Simplify $\frac{5p+10{{p}^{2}}}{10+20p-5q-10pq}$.

Algebra: Factorising and Simplifying Rational Expressions

Simplify $\frac{4{{p}^{2}}-36}{5{{p}^{2}}+8p-21}$.

Simplify $\frac{4{{p}^{2}}-36}{5{{p}^{2}}+8p-21}$.

Algebra: Cancelling Common Factors in Rational Expressions

Simplify $\frac{4x+8}{{{x}^{2}}+5x+6}$.

Factorising Quadratics to Simplify a Fraction

Simplify $\frac{2{{n}^{2}}+3n}{16n+24}$.

Simplifying Algebraic Fractions by Factorisation

Simplify $\frac{2m+6+km+3k}{{{(m+3)}^{2}}}$.

Simplify $\frac{2m+6+km+3k}{{{(m+3)}^{2}}}$.

Algebra: Reducing a Fraction with Common Factors

Simplify $\frac{{{x}^{2}}-4}{{{x}^{2}}-4x+4}$.

Simplify $\frac{{{x}^{2}}-4}{{{x}^{2}}-4x+4}$.

Algebra: Reducing a Rational Expression

Simplify $\frac{4-2x}{{{x}^{2}}-x-2}$.

Factorising to Simplify a Fraction

Simplifying a Fraction Using Factorisation

Factorise $48{{x}^{3}}+162{{y}^{3}}$ completely. Hence, simplify $\frac{48{{x}^{3}}+162{{y}^{3}}}{-12{{x}^{2}}+18xy-27{{y}^{2}}}$.

Factorise $48{{x}^{3}}+162{{y}^{3}}$ completely. Hence, simplify $\frac{48{{x}^{3}}+162{{y}^{3}}}{-12{{x}^{2}}+18xy-27{{y}^{2}}}$.

Factorisation by Special Identities

Polynomials, Cubic Equations and Partial Fractions

Factorise $125{{x}^{3}}+27{{y}^{3}}$ completely. Hence simplify $\frac{125{{x}^{3}}+27{{y}^{3}}}{25{{x}^{2}}-15xy+9{{y}^{2}}}$.
Assume $x,y$ are real and not both zero, so the denominator is nonzero.

Factorise $125{{x}^{3}}+27{{y}^{3}}$ completely. Hence simplify $\frac{125{{x}^{3}}+27{{y}^{3}}}{25{{x}^{2}}-15xy+9{{y}^{2}}}$.

Assume $x,y$ are real and not both zero, so the denominator is nonzero.

Factorise $16{{a}^{4}}-81{{b}^{6}}$ completely. Hence simplify $\frac{16{{a}^{4}}-81{{b}^{6}}}{4{{a}^{2}}+9{{b}^{3}}}$.

Factorise $16{{a}^{4}}-81{{b}^{6}}$ completely. Hence simplify $\frac{16{{a}^{4}}-81{{b}^{6}}}{4{{a}^{2}}+9{{b}^{3}}}$.

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