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Factorisation

Short Answer Type

71.

Factorise a² – 2ab + b² – c².

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72.

Factorise m⁴ – 256.

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73.

x² + 5x + 6.

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74.

Factorise y² – 7y + 12.

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75.

Factorise x² – 4x – 12.

78 Views

76.

Factorise:

3y² + 9y + 6.

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77.
Divide 33(p⁴ + 5p³ – 24p²) by 11p(p + 8).

We have 33(p⁴ + 5p³ – 24p²) $divided by$ 11p(p + 8).

 = $space fraction numerator 33 left parenthesis straight p to the power of 4 plus 5 straight p cubed minus 24 straight p squared right parenthesis over denominator 11 straight p left parenthesis straight p plus 8 right parenthesis end fraction space equals space fraction numerator 33 straight p squared left parenthesis straight p squared space plus space 5 straight p space minus space 24 right parenthesis over denominator 11 straight p space left parenthesis straight p space plus 8 right parenthesis end fraction$

 [ In numerator, p is taken out common from each term]

 = $space space space fraction numerator 33 straight p squared left square bracket straight p squared space plus space 8 straight p space minus 3 straight p space minus 24 right parenthesis over denominator 11 straight p left parenthesis straight p plus 8 right parenthesis end fraction space equals space fraction numerator 33 straight p squared left square bracket straight p left parenthesis straight p plus 8 right parenthesis minus 3 left parenthesis straight p plus 8 right parenthesis right square bracket over denominator 11 straight p left parenthesis straight p plus 8 right parenthesis end fraction$

 [In numerator, 5p is splitted in to 8p - 3p such that (8p)(-3p) = -24p]

 = $fraction numerator 33 straight p squared left square bracket left parenthesis straight p plus 8 right parenthesis left parenthesis straight p minus 3 right parenthesis right square bracket over denominator 11 straight p left parenthesis straight p space plus space 8 right parenthesis end fraction$

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 [Cancelling the factors 11p and x +8 common to both the numerator and denominator]

Thus, 33(p⁴ + 5p³ - 24p²) $divided by$ 11p(p + 8)

 = 3p(p-3)