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Mathematics

Factorise xy2 - xz2, Hence, find the value of :

(i) 9 x 82 - 9 x 22

(ii) 40 x 5.52 - 40 x 4.52

Factorisation

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Answer

xy2 - xz2

= x(y2 - z2)

Using the formula

[∵ (x2 - y2) = (x + y)(x - y)]

= x(y - z)(y + z)

Hence, xy2 - xz2 = x(y - z)(y + z)

(i) 9 x 82 - 9 x 22

= 9 x (8 - 2)(8 + 2)

= 9 x 6 x 10

= 540

Hence, 9 x 82 - 9 x 22 = 540

(ii) 40 x 5.52 - 40 x 4.52

= 40 x (5.5 - 4.5) x (5.5 + 4.5)

= 40 x 1 x 10

= 400

Hence, 40 x 5.52 - 40 x 4.52 = 400

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