Question

(3x + 2y)2 – (2x – 3y)2 . Factorise​

Answer 1

Answer

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STEP

1

:

1.1 Evaluate : (3x-2y)2 = 9x2-12xy+4y2

1.2 Evaluate : (2x-3y)2 = 4x2-12xy+9y2

STEP

2

:

Pulling out like terms

2.1 Pull out like factors :

5x2 - 5y2 = 5 • (x2 - y2)

Trying to factor as a Difference of Squares:

2.2 Factoring: x2 - y2

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 : y2 is the square of y1

Factorization is : (x + y) • (x - y)

Final result :

Final result : 5 • (x + y) • (x - y)