Aim: How do we multiply polynomials?

Do Now: Multiply the following

1. 2x(3x + 1)

2. (x – 1)(x + 2)

3. (x +2)(x2 – 3x + 1)

To multiply a binomial by a monomial , we just need to distribute 2 times

2x(3x + 1)

To multiply a binomial by another binomial , we need to the FOIL method

(x – 1)(x + 2)

= 6x2 + 2x

= x2 + 2x – x – 2 = x2 + x – 2

To multiply a trinomial by a binomial , we just need to distribute 6 times

(x + 2)(x2 – 3x + 1)

=3x2 + x + 2x2 – 3x + 2

= x3 – x2 – 2x + 2

4. 5x(x2 – 3x + 2) = 5(x2) + 5x(-3x) + 5x(2)

= 5x3 – 15x2 + 10x

5. (x2 + x – 3)(2x2 + 3x – 1)

= x2(2x2) + x2(3x) + x2(-1) + x(2x2) + x(3x) +x(-1) – 3(2x2) – 3(3x) – 3(-1)

= 2x4 + 3x3 – x2 + 2x3 + 3x2 – x – 6x2 – 9x + 3

= 2x4 + 5x3 – 4x2 – 10x + 3

Drill1. ab()

2.(3 𝑥−2)(2𝑥+5)

3.(𝑥−2)(𝑥+2)

4. (2 𝑥+1)(𝑥2−2𝑥−2)

5.(2 𝑥2+2𝑥−3)(−𝑥2−3𝑥−1)