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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~ ☆
