Question

Factorise 5a^2 -10ab +5b^2

Answer 1

find two numbers whose sum = –10

and product = ( 5 × 5 ) = 25 .

clearly, such numbers are–5 and–5.

therefore,

$5a^{2} - 10ab + 5b^{2} \\ = 5a^{2} - 5ab - 5ab + 5 {b}^{2} \\ = (5 {a}^{2} - 5ab) - (5ab - 5 {b}^{2}) \\ =5a(a - b) - 5b(a - b) \\ = (a - b)(5a - 5b).$

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