Question

Type the correct answer in each box. Consider the expressions shown below.

Answer 1

Hello!

The answer is:

- The first operation match with the polynomial:

B.  $9x^{2} -2x+2$

- The second operation match with the polynomial:

A. $-9x^{2}-2x+7$

- The third operation match with the polynomial:

C. $9x^{2} +2x-7$

Why?

In order to solve the given operations, we need to group the like terms.

Remember, like terms are terms that share the same variable and the same exponent.

For example:

$x^{2} +2x^{2} +3x^{3} +2=3x^{2} +3x^{3} +2$

We only operate with the variables that shares the same exponent.

Also, we need to remember the distributive property:

$(a+b)(c+d)=ac+ad+bc+bd$

So, we are given the following polynomials:

$A.9x^{2} -2x+7\\\\B. 9x^{2} -2x+2\\\\C. 9x^{2} +2x-7$

And we need to perform the following operations:

First operation,

$(7x^{2}-5x+3)+(2x^{2} +3x-1)=7x^{2} +2x^{2} -5x+3x+3-1\\\\7x^{2} +2x^{2} -5x+3x+3-1=9x^{2} -2x+2$

So, the first operation match with the polynomial:

B.  $9x^{2} -2x+2$

Second operation,

$(3x^{2}-4x-4)+(-12x^{2}+2x+11)=3x^{2} -12x^{2} -4x+2x-4+11\\\\3x^{2} -12x^{2} -4x+2x-4+11=-9x^{2}-2x+7$

So, the second operation match with the polynomial:

A. $-9x^{2}-2x+7$

Third operation,

$(4x^{2} -3x-9)+(5x^{2} +5x+2)=4x^{2}+5x^{2} -3x+5x-9+2\\\\4x^{2}+5x^{2} -3x+5x-9+2=9x^{2} +2x-7$

So, the second operation match with the polynomial:

C. $9x^{2} +2x-7$

Have a nice day!

Answer 2

Answer:

B, A and C.

Step-by-step explanation:

(7x^2-5x+3)+(2x^2+3x-1) is equivalent to expression B .

(3x^2-4x-4)+(-12x^2+2x+11) is equivalent to expression A .

(4x^2-3x-9)+(5x^2+5x+2) is equivalent to expression C .

You combine like terms to arrive with the answer.