Question

factorise 2a (x+y) - 4ab (x+y)​

Answer 1

Answer:

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)

Equation at the end of step

1

:

((((4•(a2))•((x2)-(y2)))-4ab•(x+y)•(x-y))+x2b2)-y2b2

STEP

2

:

Equation at the end of step

2

:

(((22a2•(x2-y2))-4ab•(x+y)•(x-y))+x2b2)-y2b2

STEP

3

:

Trying to factor as a Difference of Squares

3.1 Factoring: x2-y2

Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (x + y) • (x - y)

Equation at the end of step

3

:

((22a2•(x+y)•(x-y)-4ab•(x+y)•(x-y))+x2b2)-y2b2

STEP

4

:

4.1 Factor 4a2x2-4a2y2+4ax2b-4ay2b+x2b2-y2b2

Try to factor this 6-term polynomial into (2-term) • (3-term)

Begin by splitting the 6-term into two 3-term polynomials:

4a2x2+4ax2b+x2b2 and -4a2y2-4ay2b-y2b2

Next simplify each 3-term polynomial by pulling out like terms:

x2 • (4a2+4ab+b2) and -y2 • (4a2+4ab+b2)

Note that the two simplified polynomials have 4a2+4ab+b2 in common

Now adding the two simplified polynomials we get

(-y2+x2) • (4a2+4ab+b2) .

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