Question

Find the product (x²-a²)×(x-a)

Answer 1

step 1 :

x2 - a2

Simplify ———————

x - a

Trying to factor as a Difference of Squares :

1.1 Factoring: x2 - a2

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 : x2 is the square of x1

Check : a2 is the square of a1

Factorization is : (x + a) • (x - a)

Canceling Out :

1.2 Cancel out (x - a) which appears on both sides of the fraction line.

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Final result :

x + a

Answer 2

Answer:

x³ - ax² - a²x + a³

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