Question B.4.6: Factoring differences and sums of two cubes Factor each poly...
Factoring differences and sums of two cubes
Factor each polynomial.
a. x^{ 3 }=27 b. 8 w^{6}+125 z^{3}
a. Since x^{3}-27=x^{3}-3^{3}, we use a = x and b = 3 in the formula for factoring the difference of two cubes.
x^{3}-27=(x-3)\left(x^{2}+3 x+9\right)b. Since 8 w^{6}+125 z^{3}=\left(2 w^{2}\right)^{3}+(5 z)^{3} , we use a=2 w^{2} and b = 5z in the formula for factoring the sum of two cubes.
8 w^{6}+125 z^{3}=\left(2 w^{2}+5 z\right)\left(4 w^{4}-10 w^{2} z+25 z^{2}\right)Related Answered Questions
Question: B.4.5
Verified Answer:
a. 4x² - 1 = (2x)² - 1² Recognize t...
Question: B.4.2
Verified Answer:
a. Factor the common factor x^{2} ...
Question: B.5.6
Verified Answer:
a. \frac{x}{x-1}+\frac{2 x+3}{x^{2}-1}=\f...
Question: B.5.5
Verified Answer:
a. Compare the two denominators. Since 6ab = 2a(3b...
Question: B.5.4
Verified Answer:
a. \frac{9}{2 x} \div \frac{3}{x}=\frac{9}...
Question: B.5.3
Verified Answer:
a. \frac{2 a-2 b}{6} \cdot \frac{9 a}{a^{...
Question: B.5.2
Verified Answer:
a. \frac{2 x+4}{x^{2}+5 x+6}=\frac{2(x+2)}...
Question: B.5.1
Verified Answer:
a. The domain is the set of all real numbers excep...
Question: B.4.7
Verified Answer:
a. 2 w^{4}-32=2\left(w^{4}-16\right)[/late...
Question: B.4.4
Verified Answer:
a. Since ac = 2 ⋅ 2 = 4 and b = 5, we need two num...