Question

Factorize the following expression: x^3 y/9 - x y^3/ 16

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

((x3) • y) - 32xy3

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

x3y - 9xy3 = xy • (x2 - 9y2)

Trying to factor as a Difference of Squares:

3.2 Factoring: x2 - 9y2

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 : 9 is the square of 3

Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (x + 3y) • (x - 3y)

Final result :

xy • (x + 3y) • (x - 3y)

Terms and topics

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Canceling out