Question

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

A -9x^2-2x+7
B 9x^2-2x+2
C 9x^2+2x-7

Complete the following statements with the letter that represents the expression.

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

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

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

Answer 1

B, A and C.

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.

Answer 2

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.
`</strong>9x^(2) +2x-7<strong>`

Have a nice day!