Question

factorise this expression completely 25b² + 5bc + 1/4c²​

Answer 1

Answer:

((10b+c)^2)/4

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  

Answer 2

1 solution(s) found

See steps

Step by Step Solution

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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