Question

Factorize (2y-32y^5)​

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

2y - 25y5

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

2y - 32y5 = -2y • (16y4 - 1)

Trying to factor as a Difference of Squares:

3.2 Factoring: 16y4 - 1

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 : 16 is the square of 4

Check : 1 is the square of 1

Check : y4 is the square of y2

Factorization is : (4y2 + 1) • (4y2 - 1

Answer 2

$2y - 32 {y}^{5}$

$2y(1 - 16 {y}^{4} )$

$2y (1^2 - (4y^2)^2)$

$2y (1-4y^2)(1+4y^2)$

HOPE YOU'RE SATISFIED WITH THIS ANSWER...