Question

Simplify 16x^2 9y^2/(4x-3y)^2​

Answer 1

Hey There!!

STEP 1:

1

Simplify ——————————

(4x + 3y)2

Equation at the end of step

(4x-3y) 1

——————————————————————————— ÷ ————————

(((16•(x2))+24xy)+(9•(y2))) (4x+3y)2

STEP 2:

Equation at the end of step

2

:

(4x-3y) 1

——————————————————————— ÷ ————————

(((16•(x2))+24xy)+32y2) (4x+3y)2

STEP 3:

Equation at the end of step

(4x - 3y) 1

—————————————————————— ÷ ——————————

((24x2 + 24xy) + 32y2) (4x + 3y)2

STEP 4:

4x - 3y

Simplify —————————————————

16x2 + 24xy + 9y2

Trying to factor a multi variable polynomial :

4.1 Factoring 16x2 + 24xy + 9y2

Try to factor this multi-variable trinomial using trial and error

Found a factorization : (4x + 3y)•(4x + 3y)

Detecting a perfect square :

4.2 16x2 +24xy +9y2 is a perfect square

It factors into (4x+3y)•(4x+3y)

which is another way of writing (4x+3y)2

How to recognize a perfect square trinomial:

• It has three terms

• Two of its terms are perfect squares themselves

• The remaining term is twice the product of the square roots of the other two terms

Equation at the end of step

4:

(4x - 3y) 1

—————————— ÷ ——————————

(4x + 3y)2 (4x + 3y)2

STEP 5:

4x-3y 1

Divide ———————— by ————————

(4x+3y)2 (4x+3y)2

5.1 Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

4x - 3y 1 4x - 3y (4x + 3y)2

—————————— ÷ —————————— = —————————— • ——————————

(4x + 3y)2 (4x + 3y)2 (4x + 3y)2 1

Canceling Out :

5.2 Cancel out (4x + 3y)2 which appears on both sides of the fraction line.

Final result :

4x - 3y

Hope It Helped!~ ♡

ItsNobody~ ☆