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

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15-03-2022
Mathematics

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

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bhoopendrasisodiya34 bhoopendrasisodiya34 · Answer 1 · 2022-03-24T08:30:57+01:00

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

What is perfect square trinomials?

A trinomial which is expressed as the square of the binomial equation is a perfect square trinomial.

Let the constant term which is necessary to complete the perfect square trinomial pictured in the algebra tiles is P. Thus the trinomial can be given as,

[tex]x^2+8x+P[/tex]

Now, the algebra tiles used to represent the algebraic expression in the table form. The shape of algebra tile is square and rectangle, in which the variables represented.

The two equal factor with the middle terms being 8x can be for a trinomial (x+4). Thus,

[tex]x^2+8x+P=(x+4)^2\\x^2+8x+P=x^2+8x+4^2\\x^2+8x+P=x^2+8x+16[/tex]

Comparing both sides, we get,

[tex]P=16[/tex]

Thus, the constant term which is necessary to complete the perfect square trinomial pictured in the algebra tiles is 16.

Learn more about the perfect square trinomials here;

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