Question

What property justifies line 2 to line 3? 4 – 3x2 + 2x – x2 + 3 + x2 Line 1 4 + 3– x2 + x2 – 3x2 + 2x Line 2 7– x2 + x2 – 3x2 + 2x Line 3 7 + 0 – 3x2 + 2x Line 4 7 – 3x2 + 2x

Answer 1

Given:

The steps of simplification of the expression.

`4-3x^2+2x-x^2+3+x^2`

To find:

The properties to justify the line 2 and line 3.

Solution:

We have,

`4-3x^2+2x-x^2+3+x^2`

Line 1:
`4+3-x^2+x^2-3x^2+2x` (Rearranging the terms)

Line 2:
`7-x^2+x^2-3x^2+2x` (Combining the constant terms)

Line 3:
`7+0-3x^2+2x` (Additive inverse property)

Line 4:
`7-3x^2+2x` (Additive identity property)

Therefore, the justifications of Line 2 and Line 3 are combining the constant terms and additive inverse property respectively.