Question

factorise (a+b)^2-2(a+b)x+x^2​

Answer 1

We have,

(a+b)²-2(a+b)x+x²=0

•Regrouping the terms,

x²-2(a+b)+(a+b)²=0

•We need to express the middle term in the terms of the constant term,

»Constant Term:(a+b)²

»Middle term: -2(a+b)= -[(a+b)+(a+b)]

Now,

x²-[(a+b)+(a+b)]x+(a+b)²=0

•Opening the brackets,

→x²-(a+b)x-(a+b)x+(a+b)²=0

→x[x-(a+b)]-(a+b)[x-(a+b)]=0

→[x-(a+b)][x-(a+b)]=0

→[x-(a+b)]²=0

→x-(a+b)=0

→x=a+b

The roots of the given equation are a+b