Precalculus Skill Builders Vol 1 Solutions
Precalculus Skill Builders Vol 1 Solutions
Precalculus Skill Builders Vol 1 Solutions
Create successful ePaper yourself
Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.
9. Factoring Standard Forms<br />
Rules for Factoring<br />
Difference of Two Squares: a 2 ! b 2 = (a + b)(a ! b)<br />
Sum of Two Cubes: a 3 + b 3 = (a + b)(a 2 ! ab + b 2 )<br />
Difference of Two Cubes: a 3 ! b 3 = (a ! b)(a 2 + ab + b 2 )<br />
Special Products<br />
(a + b) 2 = a 2 + 2ab + b 2<br />
(a ! b) 2 = a 2 ! 2ab + b 2<br />
(a + b) 3 = a 3 + 3a 2 b + 3ab 2 + b 3<br />
(a ! b) 3 = a 3 ! 3a 2 b + 3ab 2 ! b 3<br />
Factor each of the following expressions.<br />
1. x 2 ! 12x + 36<br />
[ (x ! 6) 2 ]<br />
3. 9a 2 + 24a + 16<br />
[ (3a + 4) 2 ]<br />
5. (x + y) 2 ! 4(x + y) + 4<br />
[ (x + y ! 2) 2 ]<br />
7. b 2 ! 16<br />
[ (b ! 4)(b + 4) ]<br />
9. 4x 2 ! 1<br />
[ (2x ! 1)(2x + 1) ]<br />
11. s 6 ! t 6<br />
[ (s 3 ! t 3 )(s 3 + t 3 ) ]<br />
13. a 3 ! b 3<br />
[ (a ! b)(a 2 + ab + b 2 ) ]<br />
2. z 2 ! 6z + 9<br />
[ (z ! 3) 2 ]<br />
4. 16x 2 + 40xy + 25y 2<br />
[ (4x + 5y) 2 ]<br />
6. 4(a ! b) 2 ! 8(a ! b) + 4<br />
[ 4(a ! b ! 1) 2 ]<br />
8. 7x 4 ! 7<br />
[ 7 x + 1 ( ) (x ! 1)(x 2 + 1) ]<br />
10. (a ! b) 2 ! (a + b) 2<br />
[ !4ab ]<br />
12. x 3 + 1<br />
[ (x + 1)(x 2 ! x + 1) ]<br />
14. 8 p 3 + 27q 3<br />
[ (2p + 3q)(4p 2 ! 6pq + 9q 2 ) ]<br />
<strong>Skill</strong> <strong>Builders</strong>
Change language