Question

12xy (9x2 - 16y2) + 4xy (3x + 4y)​

Answer 1

Step-by-step explanation:

Changes made to your input should not affect the solution:

(1): "y2" was replaced by "y^2". 1 more similar replacement(s).

STEP

1

:

Equation at the end of step 1

(12xy•((9•(x2))-(16•(y2))))+4xy•(3x+4y)

STEP

2

:

Equation at the end of step

2

:

(12xy•((9•(x2))-24y2))+4xy•(3x+4y)

STEP

3

:

Equation at the end of step

3

:

(12xy • (32x2 - 24y2)) + 4xy • (3x + 4y)

STEP

4

:

Trying to factor as a Difference of Squares:

4.1 Factoring: 9x2-16y2

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 : 9 is the square of 3

Check : 16 is the square of 4

Check : x2 is the square of x1

Check : y2 is the square of y1

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

Equation at the end of step

4

:

12xy • (3x + 4y) • (3x - 4y) + 4xy • (3x + 4y)

STEP

5

:

Pulling out like terms

5.1 Pull out 3x+4y

After pulling out, we are left with :

(3x+4y) • ( 12xy * 1 * (3x-4y) - 4xy * (-1) ))

STEP

6

:

Pulling out like terms

6.1 Pull out like factors :

36x2y - 48xy2 + 4xy = 4xy • (9x - 12y + 1)

Final result :

4xy • (3x + 4y) • (9x - 12y + 1)