Page 586 - Algebra 1

Check
(y2 + 1)(3 - 8y)
3y2 - 8y3 + 3 - 8y Multiply using FOIL.
= 3y2 - 8y3 - 8y + 3 ✓ Commutative Property The product is the original polynomial.
Factoring with the Greatest Common Factor
Factor 45a3b - 15a3 + 15a2b - 5a2. Check your answer. SOLUTION
Example
3
= 45a3b - 15a3 + 15a2b - 5a2
= 5a2(9ab - 3a + 3b - 1)
= 5a2[(9ab - 3a) + (3b - 1)]
= 5a2[(3a)(3b - 1) + 1(3b - 1)] = 5a2[(3b - 1)(3a + 1)]
Check
Factor out the GCF.
Group into two binomials.
Factor out the GCF of each binomial. Factor out (3b - 1).
5a2[(3b - 1)(3a + 1)]
5a2[9ab + 3b - 3a - 1]
45a3b + 15a2b - 15a3 - 5a2
= 45a3b - 15a3 + 15a2b - 5a2 ✓
The product is the original polynomial.
Multiply using FOIL. Distributive Property Commutative Property
Example
4
Factoring with Opposites
Factor 3a2b - 18a + 30 - 5ab completely. Check your answer. SOLUTION
Math Reasoning
Verify Show that
5(6 - ab) is equivalent to -5(ab - 6).
3a2b - 18a + 30 - 5ab
= (3a2b - 18a) + (30 - 5ab) = 3a(ab - 6) + 5(6 - ab)
= 3a(ab - 6) + 5(-1)(ab - 6) = 3a(ab - 6) - 5(ab - 6)
= (ab - 6)(3a - 5)
Check
Group into two binomials.
Factor the GCF from each binomial. Take the opposite by multiplying by –1. Simplify.
Factor out (ab - 6).
(ab - 6)(3a - 5)
3a2b - 5ab - 18a + 30
= 3a2b - 18a + 30 - 5ab
The product is the original polynomial.
✓
Multiply using FOIL. Commutative Property
Lesson 87 571