25b² + 5bc + 1 over 4 c^2
Answers
Answer:
Step-by-step explanation:
STEP
1
:
1
Simplify —
4
Equation at the end of step
1
:
1
((25 • (b2)) + 5bc) + (— • c2)
4
STEP
2
:
Equation at the end of step 2
c2
((25 • (b2)) + 5bc) + ——
4
STEP
3
:
Equation at the end of step
3
:
c2
(52b2 + 5bc) + ——
4
STEP
4
:
Rewriting the whole as an Equivalent Fraction
4.1 Adding a fraction to a whole
Rewrite the whole as a fraction using 4 as the denominator :
25b2 + 5bc (25b2 + 5bc) • 4
25b2 + 5bc = —————————— = ————————————————
1 4
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
STEP
5
:
Pulling out like terms
5.1 Pull out like factors :
25b2 + 5bc = 5b • (5b + c)
Adding fractions that have a common denominator :
5.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
5b • (5b+c) • 4 + c2 100b2 + 20bc + c2
———————————————————— = —————————————————
4 4
Trying to factor a multi variable polynomial :
5.3 Factoring 100b2 + 20bc + c2
Try to factor this multi-variable trinomial using trial and error
Found a factorization : (10b + c)•(10b + c)
Detecting a perfect square :
5.4 100b2 +20bc +c2 is a perfect square
It factors into (10b+c)•(10b+c)
which is another way of writing (10b+c)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 :
(10b + c)2
——————————
4
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