Question

What constant term is necessary to complete the perfect square trinomial pictured in the algebra tiles? x2 8x.

Answer 1

The constant term that is necessary to complete the perfect square trinomial pictured in the algebra tile is 16.

What is a perfect square trinomial?

A perfect square trinomial is an algebraic statement with three terms of the type ax²+bx+c. It is calculated by multiplying a binomial with itself.

For the given trinomial to be a perfect square trinomial, the value of the constant term should be such that the value of the term expression must be similar to (a+b)². Therefore,

$(a+b)^2=a^2+2ab+b^2$

            $=x^2+8x$

Now, if we compare the two equations we will understand that the first term of the perfect square trinomial is x, and thus, the last term should 16.

$(x+4)^2 = x^2+8x+16$

hence, the constant term that is necessary to complete the perfect square trinomial pictured in the algebra tile is 16.

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