Find the greatest common factor. 2y^3, 8y

Mathematics

1 answer:

Ira Lisetskai [31]3 years ago

4 0

Answer:

STEP1:Equation at the end of step 1

2y3 - 8y

STEP2:

STEP3:Pulling out like terms

3.1 Pull out like factors :

2y3 - 8y = 2y • (y2 - 4)

Trying to factor as a Difference of Squares:

3.2 Factoring: y2 - 4

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 : y2 is the square of y1

Factorization is : (y + 2) • (y - 2)

Final result :

2y • (y + 2) • (y - 2)

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