Question

$(x { }^{2} - a {}^{2} ) \times (x - a)$
​

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.

Factorization is :

Canceling Out : ( x + a) . ( x - a )

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

Final result :

x + a