Question

factorise 32(x+y)2 -2x-2y​

Answer 1

Answer:

Step by Step Solution:

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STEP

1

:

Equation at the end of step 1

(32 • (x2)) - (2•32y2)

STEP

2

:

Equation at the end of step

2

:

25x2 - (2•32y2)

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

32x2 - 18y2 = 2 • (16x2 - 9y2)

Trying to factor as a Difference of Squares:

4.2 Factoring: 16x2 - 9y2

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 : 16 is the square of 4

Check : 9 is the square of 3

Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (4x + 3y) • (4x - 3y)

Final result :

2 • (4x + 3y) • (4x - 3y)

Answer 2

Step-by-step explanation:

64(x+y)-2(x+y)

(x+y)(64-2)

(x+y)62

62x+62y