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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)

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106.
Factorise the expression and divide them as directed.

39y³(50y² - 98) $divided by$ 26y²(5y + 7)

∵             50y² - 98 = 2(25y² - 49)

                            = 2[(5y)² - (7)²]

                            =2[(5y - 7)(5y + 7)]

∴ $fraction numerator 39 straight y cubed left parenthesis 50 straight y squared minus 98 right parenthesis over denominator 26 straight y squared left parenthesis 5 straight y space plus space 7 right parenthesis end fraction space equals space fraction numerator 3 cross times 13 cross times straight y cross times straight y cross times straight y cross times 2 cross times left parenthesis 5 straight y minus 7 right parenthesis cross times left parenthesis 5 straight y plus 7 right parenthesis over denominator 2 cross times 13 cross times straight y cross times straight y cross times left parenthesis 5 straight y space plus space 7 right parenthesis end fraction$

= $fraction numerator 3 cross times straight y cross times left parenthesis 5 straight y minus 7 right parenthesis over denominator 1 end fraction$

Thus, 39y³(50y² - 98) / 26y²(5y + 7) = 3y(5y - 7)