Question

factorize x^2 + x^2y^2 - 132y^2​

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

((x4)-((x2)•(y2)))-(22•3•11y4)

STEP

2

:

Trying to factor a multi variable polynomial

2.1 Factoring x4 - x2y2 - 132y4

Try to factor this multi-variable trinomial using trial and error

Found a factorization : (x2 + 11y2)•(x2 - 12y2)

Trying to factor as a Difference of Squares:

2.2 Factoring: x2-12y2

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 : 12 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Final result :

(x2 + 11y2) • (x2 - 12y2)