Question

(x-y) 2-6(x-y)+5 factorise it

Answer 1

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Answer 2

Correct Question :-

Factorise (x - y)² - 6(x - y) + 5

Answer :-

(x - y - 5)(x - y - 1)

Solution :-

(x - y)² - 6(x - y) - 5

Let us assume x - y = z

By substituting x - y as z in the above expression

= (z)² - 6(z) + 5

= z² - 6z + 5

Splitting the middle term

First multiply the first and last terms

z² * 5 = 5z²

Now find the factors of 5z² which sums to middle term i.e 5z²

- 5z * - z = 5z² ( - 5z - z = - 6z)

- 5z and - z are the factors which sums to middle term i.e - 6z

Now replace - 6z with - 5z - z

= z² - 5z - z + 5

= z(z - 5) - 1(z - 5)

= (z - 5)(z - 1)

Now substitute z = x - y in the above expression

= (x - y - 5)(x - y - 1)