Enter the correct value so that each expression is a perfect-square trinomial. x² - 10x + __

Solution:

Perfect square trinomials are algebraic expressions with three terms that are obtained by multiplying a binomial with the same binomial.

A perfect square is a number that is obtained by multiplying a number by itself.

Binomials are algebraic expressions consisting of just two terms that are either separated by a positive (+) or a negative (-) sign.

Let us consider

x² - 10x + A

We have to find the expression here

The equation is of the form (a - b)² = a² - 2ab + b²

By comparing it

a = x

-2ab = -10x

⇒ -2xb = -10x

⇒ b = 5

We have to square b to obtain perfect square trinomial

b² = 25

Therefore, the correct value is 25.

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Enter the correct value so that each expression is a perfect-square trinomial. x² - 10x + __

Summary:

The correct value which makes each expression a perfect-square trinomial is x² - 10x + 25.