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Factorisation

Short Answer Type

101.

Factorise the expression and divide them as directed.

$left parenthesis straight m squared space minus space 14 straight m space minus space 32 right parenthesis space divided by space left parenthesis straight m space plus space 2 right parenthesis$

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102.

Factorise the expression and divide them as directed.

(5p² - 25p + 20) $divided by$ (p - 1)

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103.

Factorise the expressions and divide them as directed.

4yz(z² + 6z - 16) $divided by$ 2y(z + 8)

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104.

Factorise the expression and divide them as directed.

5pq(p² - q²) $divided by$ 2p(p + q)

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105.
Factorise the expression and divide them as directed.

12xy(9x² - 16y²) $divided by$ 4xy(3x + 4y)

∵ 9x² - 16y² = (3x)² - (4y)²

= (3x - 4y)(3x + 4y)

∴ $fraction numerator 12 xy left parenthesis 9 straight x squared minus 16 straight y squared right parenthesis over denominator 4 xy left parenthesis 3 straight x plus 4 straight y right parenthesis end fraction equals fraction numerator 2 cross times 2 cross times 3 cross times straight x cross times straight y cross times left parenthesis 3 straight x minus 4 straight y right parenthesis cross times left parenthesis 3 straight x plus 4 straight y right parenthesis over denominator 2 cross times 2 cross times straight x cross times straight y cross times left parenthesis 3 straight x plus 4 straight y right parenthesis end fraction$

= $space space space space fraction numerator 3 cross times left parenthesis 3 straight x space minus space 4 straight y right parenthesis over denominator 1 end fraction$

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