Question

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

Answer 1

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

Answer 2

Answer:

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

Step-by-step 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