Question

Factorise 16x^4-64y^4​

Answer 1

STEP

1

:

Equation at the end of step 1

(16 • (x4)) - 26y8

STEP

2

:

Equation at the end of step

2

:

24x4 - 26y8

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

16x4 - 64y8 = 16 • (x4 - 4y8)

Trying to factor as a Difference of Squares:

4.2 Factoring: x4 - 4y8

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 : 4 is the square of 2

Check : x4 is the square of x2

Check : y8 is the square of y4

Factorization is : (x2 + 2y4) • (x2 - 2y4)

Trying to factor as a Difference of Squares:

4.3 Factoring: x2 - 2y4

Check : 2 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Final result :

16 • (x2 + 2y4) • (x2 - 2y4)