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Algebra 2
Section 4.2
Simplifying Products
and Quotients
Simplify.
1. 10y – 20
25y - 75
2. 4 – c2
5c - 10
2
= 10(y – 2)
5 25(y – 3)
= 2(y – 2)
5(y – 3)
factor out GCF
= -c2 + 4 switch around 4 – c2
5c - 10
= -1(c2 – 4) factor out common factor
5(c – 2)
= -1(c + 2)(c – 2) difference of 2 squares
5(c – 2)
= - (c + 2)
5
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3. 6x2 – 30x + 24
10x2 – 100x + 240
=
– 5x + 4)
10(x2 – 10x + 24)
6(x2
3
= 6(x – 4)(x – 1)
10(x – 6)(x – 4)
factor out GCF
factor into two binomials
1
2
3a4
5y2z
4. -xy · 4a2
6a6 -5xy3z
= 2
15a4y2z
multiply across
what’s left
5
= 3(x – 1)
5(x – 6)
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5. 9c3 · 2x + 8
8x + 32 -3c4
3
6. - 4a + 8 6 – 3a
-2x – 10 x2 - 25
1
2 – 25
=
4a
+
8
·
x
=
· 2(x + 4)
8(x + 4) -3c4 factor where possible -2x – 10 -3a + 6
9c3
4
= 3
- 4c
-c
multiply across
what’s left
multiply by reciprocal
2
= - 4(a – 2) · (x + 5)(x – 5)
-2(x + 5)
-3(a – 2) factor where
possible
1
= 2(x - 5)
-3
multiply across
what’s left
© Mr. Sims
Simplify.
Algebra 2
Section 4.2
Assignment
1.) 3a  15
10  2a
2
2.) 3n  21n  36
2n 2  4n  48
2
3.) 5y  15y  50
50  2y 2
4
5bc
3
4.)

3 10ab4c
5.) 7x  35  9x  45
15n
10n 2
2
6.) 5a  25  2a  2a  60
4a 12
a 2  3a
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