(x² +8 xy + 16 y 2) = (X+4Y)
Answers
Answer:
(x + 4y)3
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9
Step-by-step explanation:
STEP
1
:
x + 4y
Simplify ——————
3
Equation at the end of step
1
:
((((x2)+8xy)+(16•(y2)))1) (x+4y)
—————————————————————————•——————
3 3
STEP
2
:
Equation at the end of step
2
:
((((x2)+8xy)+(24y2))1) (x+4y)
——————————————————————•——————
3 3
STEP
3
:
x2 + 8xy + 16y2
Simplify ———————————————
3
Trying to factor a multi variable polynomial :
3.1 Factoring x2 + 8xy + 16y2
Try to factor this multi-variable trinomial using trial and error
Found a factorization : (x + 4y)•(x + 4y)
Detecting a perfect square :
3.2 x2 +8xy +16y2 is a perfect square
It factors into (x+4y)•(x+4y)
which is another way of writing (x+4y)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
3
:
(x + 4y)2 (x + 4y)
————————— • ————————
3 3
STEP
4
:
Multiplying Exponential Expressions:
4.1 Multiply (x+4y)2 by (x+4y)
The rule says : To multiply exponential expressions which have the same base, add up their exponents.
In our case, the common base is (x+4y) and the exponents are :
2
and 1 , as (x+4y) is the same number as (x+4y)1
The product is therefore, (x+4y)(2+1) = (x+4y)3
Final result :
(x + 4y)3
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9
Answer:
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