which are perfect trinomial square write yes or no 49m^2+140mn+100n^2
Answers
Answer:
yes it is a perfect square.
its not a trinomial perfect square though..
STEP
1
:
Equation at the end of step 1
((49 • (m2)) + 140mn) + (22•52n2)
STEP
2
:
Equation at the end of step
2
:
(72m2 + 140mn) + (22•52n2)
STEP
3
:
Trying to factor a multi variable polynomial
3.1 Factoring 49m2 + 140mn + 100n2
Try to factor this multi-variable trinomial using trial and error
Found a factorization : (7m + 10n)•(7m + 10n)
Detecting a perfect square :
3.2 49m2 +140mn +100n2 is a perfect square
It factors into (7m+10n)•(7m+10n)
which is another way of writing (7m+10n)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
Final result :
(7m + 10n)2
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Answer:
(a+b)²=a²+2ab+b²
a²=49m²
2ab=140mn
b²=100n²
a=√49m²√7×7×m×m
a=7m
b=√100n²√10×10×n×n
b=10n
2ab=2×7m×10n
2ab=140mn
yes it is a perfect trinomial square