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Factorisation

Short Answer Type

131.

Find and correct the errors in the following mathematical statement.

(a - 4) (a -2) = a² - 8

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132.

Find and correct the errors in the following mathematical statement.

$fraction numerator 3 straight x squared over denominator 3 straight x squared end fraction space equals space 0$

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133.

Find and correct the errors in the following mathematical statement.

$space space fraction numerator 3 straight x squared plus 1 over denominator 3 straight x squared end fraction space equals space 1 space plus space 1 space equals space 2$

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134.

Find and correct the errors in the following mathematical statement.

$fraction numerator 3 straight x over denominator 3 straight x plus 2 end fraction equals 1 half$

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135.

Find and correct the errors in the following mathematical statement.

$fraction numerator 3 over denominator 4 straight x plus 3 end fraction space equals space fraction numerator 1 over denominator 4 straight x end fraction$

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136.

Find and correct the errors in the following mathematical statement.

$fraction numerator 4 straight x plus 5 over denominator 4 straight x space end fraction space equals space 5$

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137.

Find and correct the errors in the following mathematical statement.

$fraction numerator 7 straight x plus 5 over denominator 5 end fraction space equals space 7 straight x$

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138.
Factorise: 27x³ - 21x² + 15x⁴

We have    27x³= 3 × 3 × 3 × x × x × x

               21x² = 3 × 7 × x × x

               15x⁴ = 3 × 5 × x × x × x × x

We get common factors as 3, x and x.

i.e.      3 × x × x    or      3x²

∴                                          27x³ = 3x² × 3 × x × 3 = 3x² × 9x

                                            21x² = 3x² × 7 = 3x² × 7

                                            15x⁴ = 3x² × 5 × x × x = 3x² × 5x²

$rightwards double arrow$ 27x³ - 21x² + 15x⁴ = (3x² × 9x) - (3x² × 7) + (3x² × 5x²)

                                  = 3x²[9x - 7 + 5x²]