Question

Factorise : 25x^4 - 60x^2y^2 + 36y^4​

Answer 1

Step-by-step explanation:

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Answer 2

STEP

1

:

Equation at the end of step 1

((25•(x4))-((60•(x2))•(y2)))+(22•32y4)

STEP

2

:

Equation at the end of step

2

:

((25 • (x4)) - ((22•3•5x2) • y2)) + (22•32y4)

STEP

3

:

Equation at the end of step

3

:

(52x4 - (22•3•5x2y2)) + (22•32y4)

STEP

4

:

Trying to factor a multi variable polynomial

4.1 Factoring 25x4 - 60x2y2 + 36y4

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

Found a factorization : (5x2 - 6y2)•(5x2 - 6y2Theory : 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.