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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