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3 years ago

Express the sum of the polymonial 3x^2+15x-56 and the square of the binomial (x-8) as a polynomial in standard form.

Mathematics

1 answer:

tester [92]3 years ago

7 0

Given:

Polynomial is $3x^2+15x-56$ .

To find:

The sum of given polynomial and the square of the binomial (x-8) as a polynomial in standard form.

Solution:

The sum of given polynomial and the square of the binomial (x-8) is

$3x^2+15x-56+(x-8)^2$

$=3x^2+15x-56+x^2-2(x)(8)+8^2$ $[\because (a-b)^2=a^2-2ab+b^2]$

$=3x^2+15x-56+x^2-16x+64$

On combining like terms, we get

$=(3x^2+x^2)+(15x-16x)+(-56+64)$

$=4x^2-x+8$

Therefore, the sum of given polynomial and the square of the binomial (x-8) as a polynomial in standard form is $4x^2-x+8$ .

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