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Factorisation Using Algebraic Identities

vi Factorise ...

Question

Question 1(vi)
Factorise the following expressions
$121 b^{2} - 88 b c + 16 c^{2}$

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Solution

$121 b^{2} - 88 b c + 16 c^{2} = (11 b)^{2} - 2 (11 b) (4 c) + (4 c)^{2} = (11 b - 4 c)^{2} [(a - b)^{2} = a^{2} - 2 a b + b^{2}]$

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121 b^{2} - 88 b c + 16 c^{2}

121 b^{2} + 88 b c + 16 c^{2}

121 b^{2} - 88 b c + 16 c^{2}

a^{2} + 8 a + 16

p^{2} - 10 p + 25

25 m^{2} + 30 m + 9

49 y^{2} + 84 y z + 36 z^{2}

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121 b^{2} - 88 b c + 16 c^{2}

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Factorise the following expressions.

(i) a² + 8a + 16

(ii) p² − 10p + 25

(iii) 25m² + 30m + 9

(iv) 49y² + 84yz + 36z²

(v) 4x² − 8x + 4

(vi) 121b² − 88bc + 16c²

(vii) (l + m)² − 4lm (Hint: Expand (l + m)² first)

(viii) a⁴ + 2a²b² + b⁴

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