Question

50ax^2-32ay^2 (step by step)

Answer 1

Step-by-step explanation:

Step by Step Solution

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STEP

1

:

Equation at the end of step 1

(50 • (x2)) - 25y2

STEP

2

:

Equation at the end of step

2

:

(2•52x2) - 25y2

STEP

3

:

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

50x2 - 32y2 = 2 • (25x2 - 16y2)

Trying to factor as a Difference of Squares:

4.2 Factoring: 25x2 - 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 : 25 is the square of 5

Check : 16 is the square of 4

Check : x2 is the square of x1

Check : y2 is the square of y1

Factorization is : (5x + 4y) • (5x - 4y)

Final result :

2 • (5x + 4y) • (5x - 4y)

Answer 2

Answer:

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2a (5x+4y) (5x–4y)

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