Factories the given algebraic expression by taking out the common terms. Also, write the common term
$8 a b + 14 a^{2} b - 2 a^{3} - 12 a b^{2}$

Open in App

Solution

We first factorize each term of the given expression $8 a b + 14 a^{2} b - 2 a^{3} - 12 a b^{2}$ as shown below:

$8 a b = 2 \times 2 \times 2 \times a \times b 14 a^{2} b = 2 \times 7 \times a \times a \times b 2 a^{3} = 2 \times a \times a \times a 12 a b^{2} = 2 \times 2 \times 3 \times a \times b \times b$

The common factors are $2$ and $a$ , therefore, the HCF is $2 \times a = 2 a$ .

Now, by taking out the common term(HCF), we have:

$8 a b + 14 a^{2} b - 2 a^{3} - 12 a b^{2} = 2 a (4 b + 7 a b - 2 a^{2} - 6 b^{2})$

Hence, the common term is $2 a$ .

Suggest Corrections

Similar questions

5 p q + 20 p^{3} q^{3} - 15 p^{2} q

4 x^{2} y^{2} - 7 x y + 4

12 x^{2} + 5 x - 8

Find and algebraic expression to compute the sum of the first n terms of the arithmetic sequence with first term f and common difference d.

The first term of an arithmetic sequence is 6 and common difference is 4. Then the algebraic expression for sum of the first 'n' terms its.

Join BYJU'S Learning Program