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Wize High School Grade 12 Calculus Textbook > Review
Factoring
Linear Equations (Lines)
Previous Section
Radical Expressions
Next Section
Factoring w/ Identities
Extra Practice
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Show Solutions
Factoring w/ Identities
Difference of Squares
a
2
−
b
2
=
(
a
−
b
)
(
a
+
b
)
a^2-b^2=\left(a-b\right)\left(a+b\right)
a
2
−
b
2
=
(
a
−
b
)
(
a
+
b
)
Difference of Cubes
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
a
b
+
b
2
)
a^3-b^3=\left(a-b\right)\left(a^2+ab+b^2\right)
a
3
−
b
3
=
(
a
−
b
)
(
a
2
+
ab
+
b
2
)
Sum of Cubes
a
3
+
b
3
=
(
a
+
b
)
(
a
2
−
a
b
+
b
2
)
a^3+b^3=\left(a+b\right)\left(a^2-ab+b^2\right)
a
3
+
b
3
=
(
a
+
b
)
(
a
2
−
ab
+
b
2
)
Example
Factor the following:
a)
x
2
−
4
x^2-4
x
2
−
4
(
x
−
2
)
(
x
+
2
)
\left(x-2\right)\left(x+2\right)
(
x
−
2
)
(
x
+
2
)
b)
x
3
−
27
x^3-27
x
3
−
27
(
x
−
3
)
(
x
2
+
3
x
+
9
)
\left(x-3\right)\left(x^2+3x+9\right)
(
x
−
3
)
(
x
2
+
3
x
+
9
)
c)
(
x
+
1
)
3
+
8
\left(x+1\right)^3+8
(
x
+
1
)
3
+
8
(
(
x
+
1
)
+
2
)
(
(
x
+
1
)
2
−
(
x
+
1
)
(
2
)
+
4
)
\left(\left(x+1\right)+2\right)\left(\left(x+1\right)^2-\left(x+1\right)\left(2\right)+4\right)
(
(
x
+
1
)
+
2
)
(
(
x
+
1
)
2
−
(
x
+
1
)
(
2
)
+
4
)
=
(
x
+
3
)
(
x
2
+
2
x
+
1
−
2
x
−
2
+
4
)
=\left(x+3\right)\left(x^2+2x+1-2x-2+4\right)
=
(
x
+
3
)
(
x
2
+
2
x
+
1
−
2
x
−
2
+
4
)
=
(
x
+
3
)
(
x
2
+
3
)
=\left(x+3\right)\left(x^2+3\right)
=
(
x
+
3
)
(
x
2
+
3
)
d)
x
4
−
16
x^4-16
x
4
−
16
This is a difference of squares
(
x
2
)
2
−
(
4
)
2
\left(x^2\right)^2-\left(4\right)^2
(
x
2
)
2
−
(
4
)
2
:
(
x
2
−
4
)
(
x
2
+
4
)
\left(x^2-4\right)\left(x^2+4\right)
(
x
2
−
4
)
(
x
2
+
4
)
=
(
x
−
2
)
(
x
+
2
)
(
x
2
+
4
)
=\left(x-2\right)\left(x+2\right)\left(x^2+4\right)
=
(
x
−
2
)
(
x
+
2
)
(
x
2
+
4
)
Extra Practice
Factoring (Review)
Practice: Factoring
Factor
625
x
4
−
16
y
4
625x^4-16y^4
625
x
4
−
16
y
4
Factoring (Review)
Practice: Factoring
Factor
27
x
3
−
y
3
27x^3-y^3
27
x
3
−
y
3
Factoring (Review)
Practice: Factoring
Factor
5
x
2
−
31
x
+
6
5x^2-31x+6
5
x
2
−
31
x
+
6
Factoring (Review)
Practice: Factoring
Factor
3
x
2
−
13
x
−
10
3x^2-13x-10
3
x
2
−
13
x
−
10
Factoring
Practice: Factoring
Factor
x
2
−
10
x
+
21
x^2-10x+21
x
2
−
10
x
+
21
Factoring
Practice: Factoring
Factor
x
2
−
9
x
−
10
x^2-9x-10
x
2
−
9
x
−
10
