Question

factorize 49x_64x

answer please
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Answer 1

STEP 1:

Pulling out like terms

3.1     Pull out like factors :

  49x3 - 64x  =   x • (49x2 - 64)  

Trying to factor as a Difference of Squares:

3.2      Factoring:  49x2 - 64  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  49  is the square of  7  

Check : 64 is the square of 8

Check :  x2  is the square of  x1  

Factorization is :       (7x + 8)  *  (7x - 8)

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Answer 2

Explanation:

1. (7x)^2 -( 4x)^2
2. (7x+4x) (7x-4x) [Formula - a^2 - b^2 =( a+b ) ( a-b)
3. So, the required ans is (7x+4x) (7x-4x)

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