Mathematical Statement Justification −2(2x3 + 4x2 − 3) + 5(x2 − 2x − 2) Given −4x3 − 8x2 + 6 + 5x2 − 10x − 10 −4x3 − 8x2 + 5x2 − 10x + 6 − 10 −4x3 − 3x2 − 10x − 4

The answer is given below

Explanation:

The distributive property states that:

a(b + c) = ab + ac

The commutative property states that:

a + b = b + a   and ab = ba

For a function, the coefficients of the same degree are added.

When collecting like terms, terms of the same degree are arranged together and the terms are usually arranged in order of decreasing degree (or increasing degree)

Mathematical Statement                                               Justification

−2(2x³ + 4x² − 3) + 5(x² − 2x − 2)                                 Given

−4x³ − 8x² + 6 + 5x² − 10x − 10                                    Distributive property

−4x³ − 8x² + 5x² − 10x + 6 − 10                                    Collecting like terms

−4x³ − 3x² − 10x − 4                                                      Commutative property

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