# a(b + c) = ab + ac MULTIPLYING POLYNOMIALS (Equivalent Algebraic Expressions)

```MCR3U1
MULTIPLYING POLYNOMIALS
(Equivalent Algebraic Expressions)
Unit 1 L2
Recall the distributive property:
a(b + c) = ab + ac
Ex 
Expand and simplify each of the following:
a)
2𝑥(3𝑥 2 + 5𝑥 − 8)
b)
(𝑚 − 4)(4𝑚 + 3)
c)
(3𝑦 − 4)(3𝑦 + 4)
d)
(3𝑥 − 2)2
SHORT-CUTS:
(𝑥 &plusmn; 𝑦)2 = 𝑥 2 &plusmn; 2𝑥𝑦 + 𝑦 2
(𝑥 − 𝑦)(𝑥 + 𝑦) = 𝑥 2 − 𝑦 2
With the use of the distributive property, the product of two (or more) polynomials can be
found by multiplying each term in one polynomial by each term in the other.
Ex 
Expand and simplify each of the following:
a)
4(3𝑥 − 1)2
c)
3(2𝑥 − 1)(2𝑥 + 1) − (3𝑥 + 1)(𝑥 − 5) + 4(2𝑥 − 3)2
b)
(𝑥 − 4)(2𝑥 + 5)(3𝑥 − 1)
MCR3U1
Unit 1 L2
Since polynomials behave like numbers, the multiplication of polynomials has the same
properties.
For any polynomials a, b, and c:
i)
ii)
iii)
Ex 
Ex 
ab = ba
(ab)c = a(bc)
a(b+c) = ab+ac
(commutative property)
(associative property)
(distributive property)
Verify the commutative and associative properties for polynomials:
(a + b)(a + b + c)
vs.
(a + b + c)(a + b)
[3x(x – 4)](x + 4)
vs.
3x[(x – 4)(x + 4)]
Decide whether the following expressions are equivalent:
3(𝑦 − 2𝑥)3 and −24𝑥 3 + 36𝑥 2 𝑦 − 18𝑥𝑦 2 + 3𝑦 3
HOMEWORK: p.95–97 #4ace, 5, 6c, 9, 10, 11ad, 14
```