Name ______________________________________ Date _____________________ Hour _______

H-03 Multiplying Polynomials

Part 2

Warm-up: Simplify each expression by combining like terms and/or multiplying polynomials.

1. (3𝑥2 + 2𝑥 − 5) + (2𝑥2 − 2𝑥 + 10) 2. (3𝑥2 + 2𝑥 − 5) − (2𝑥2 − 2𝑥 + 10)

3. 2𝑥(10𝑥2 − 5𝑥 + 4) 4. −1

2𝑥2(−10𝑥2 + 8𝑥 − 2)

5. (2𝑥 + 1)(𝑥 − 5) 6. (3𝑥 − 2)(3𝑥 − 2)

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Remember the difference between addition/subtraction and multiplication:

Addition/Subtraction Multiplication

- only works for ________ terms - works for _________ terms

- ________ coefficients - ______________ coefficients

- ________ exponent rules - _______ exponent rules (you _____ them)

Recall: What does it mean to square something? For example, 32 means what?

When we did the exponents unit, we talked about how having an exponent outside of parentheses

technically meant we had to multiply the whole base to itself.

(2𝑥2𝑦)2 = _____________________

Then we allowed a rule to distribute that allowed us to “cheat”.

This cheat does not work for polynomials. You can only cheat if you have a product or quotient being

raised to a power. You cannot cheat if you have a sum or difference raised to a power.

So, what do we do when we have a sum or difference raised to a power? Rewrite the problem and

distribute!

1A. (2𝑥 + 1)2

1B. (3𝑥 + 4)2

2A. (4𝑥 − 2)2

2B. (5𝑥 − 1)2

The largest product I will ask you to multiply out is a binomial multiplied to a trinomial. There is a lot of

work involved in this, so you need to show as much work as possible to avoid simple errors.

3A. (𝑎 + 3)(2𝑎2 − 𝑎 + 5) 3B.(𝑎 − 2)(3𝑎2 + 2𝑎 − 1)

4A. (2𝑎2 − 4)(𝑎2 − 5𝑎 + 4) 4B. (3𝑎2 + 3)(2𝑎2 − 7𝑎 + 10)