Question

factorize: 16a4 – 4a2 – 4a – 1

Answer 1

Step-by-step explanation:

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Answer 2

Concept

Factoring an algebraic expression means writing the given expression as the product of its factors. These factors can be numbers, variables, or algebraic expressions.

There are four ways to factor algebraic expressions.

• Common divisor method

• How to regroup terms  

• Factoring by ID

• Factor of the form (x+a) (x+b)

Regrouping means rearranging the specified expressions based on the same or similar terms.

Given

We have been given an equation $16a^4-4a^2-4a-1$ .

Find

We are asked to determine the factor of the given equation.

Solution

We will solve this question by grouping method

Add and subtract $8a^3$ and $4a^2$ in the given equation , we get

$16a^4-4a^2-4a-1+8a^3-8a^3+4a^2-4a^2=0$

On rearranging , we get

$16a^4+8a^3+4a^2-8a^3-4a^2-2a-4a^2-2a-1=0\\\\4(4a^4+2a^3+a^2)-2(4a^3+2a^2+a)-1(4a^2+2a+1)\\\\4a^2(4a^2+2a+1)-2a(4a^2+2a+1)-1(4a^2+2a+1)\\\\(4a^2+2a+1)((4a^2-2a-1)$

Therefore , the factorization of the given equation is $(4a^2+2a+1)((4a^2-2a-1)$ .

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