Question

Enter the correct value so that each expression is a perfect-square trinomial.

x2 – 10x +_____

Answer 1

the answer is x2-10x+25 because that is half of -10 (5) squared

Answer 2

A = 25 so that the expression
`x^2-10x+A` is a perfect-square trinomial.

Explanation:

Given : expression
`x^2-10x+A`

We have to find the value of A so that each expression is a perfect-square trinomial.

perfect-square is the term in the form of
`(a+b)^2 \ or\ (a-b)^2`

Since , we know the algebraic identity,

`(a+b)^2=a^2+b^2+2ab\\\\ (a-b)^2=a^2+b^2-2ab`

Given expression
`x^2-10x+A` is of the form of
`(a-b)^2=a^2+b^2-2ab`

Thus, comparing , we get,

a= x ,

-2ab = -10x

⇒ b = 5

Thus adding b² term to get perfect-square trinomial.

b² = 25

Thus, the perfect-square trinomial becomes
`x^2-10x+25=(x-5)^2`

So, A = 25