Q. 6.8

Question

Factor: $8 a^{3} b + 2 a^{2} b^{2} - 6 a b^{3}$ .

Step-by-Step Solution

Verified

Answer

The factored form is $\begin{array}{rcl} 2 a b (4 a^{2} + a b - 3 b^{2}) \end{array}$

1Step 1. Given Information

The given information is $8 a^{3} b + 2 a^{2} b^{2} - 6 a b^{3}$ .

2Step 2. Find GCF of the terms

Factor each of the terms in the given expression.

$8 a^{3} b = 2 \cdot 2 \cdot 2 \cdot a \cdot a \cdot a \cdot b 2 a^{2} b^{2} = 2 \cdot a \cdot a \cdot b \cdot b 6 a b^{3} = 2 \cdot 3 \cdot a \cdot b \cdot b \cdot b$

From the obtained factors, it is observed that the common factors are $2, a, b$ .
Multiply the common factors to determine the GCF of the terms of the given expression.

$2 \cdot a \cdot b = 2 a b$

So, the GCF of the terms of the given expression is $2 a b$ .

3Step 3. Rewrite the given expression

Express each of the term of the given expression as a product of GCF, $2 a b$ .

$2 a b \cdot 4 a^{2} + 2 a b \cdot a b - 2 a b \cdot 3 b^{2}$

Use the reverse distributive property, $a b + a c = a (b + c)$ to rewrite the obtained expression.

$2 a b \cdot 4 a^{2} + 2 a b \cdot a b - 2 a b \cdot 3 b^{2} = 2 a b (4 a^{2} + a b - 3 b^{2})$

4Step 4. Check

Multiply the obtained factors.

$\begin{array}{rcl} 2 a b (4 a^{2} + a b - 3 b^{2}) & = & 2 a b \cdot 4 a^{2} + 2 a b \cdot a b - 2 a b \cdot 3 b^{2} \\ = & 8 a^{3} b + 2 a^{2} b^{2} - 6 a b^{3} \end{array}$

Since the obtained expression is the same as the given expression, the obtained factors are verified.

Q. 6.7

Q. 6.9

Other exercises in this chapter

Factor: 15x3y-3x2y2+6xy3

Factor: -7a3+21a2-14a

View solution