Question

factorise: p²+p+¼

please help me solve and send. ​

Answer 1

Answer:

answer is (p+1/2)² according to the question

Answer 2

Answer:

Final result :

(2p - 1)2

—————————

4

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Step-by-step explanation:

STEP

1

:

1

Simplify —

4

Equation at the end of step

1

:

1

((p2) - p) + —

4

STEP

2

:

Rewriting the whole as an Equivalent Fraction

2.1 Adding a fraction to a whole

Rewrite the whole as a fraction using 4 as the denominator :

p2 - p (p2 - p) • 4

p2 - p = —————— = ————————————

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

3

:

Pulling out like terms

3.1 Pull out like factors :

p2 - p = p • (p - 1)

Adding fractions that have a common denominator :

3.2 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:

p • (p-1) • 4 + 1 4p2 - 4p + 1

————————————————— = ————————————

4 4

Trying to factor by splitting the middle term

3.3 Factoring 4p2 - 4p + 1

The first term is, 4p2 its coefficient is 4 .

The middle term is, -4p its coefficient is -4 .

The last term, "the constant", is +1

Step-1 : Multiply the coefficient of the first term by the constant 4 • 1 = 4

Step-2 : Find two factors of 4 whose sum equals the coefficient of the middle term, which is -4 .

-4 + -1 = -5

-2 + -2 = -4 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and -2

4p2 - 2p - 2p - 1

Step-4 : Add up the first 2 terms, pulling out like factors :

2p • (2p-1)

Add up the last 2 terms, pulling out common factors :

1 • (2p-1)

Step-5 : Add up the four terms of step 4 :

(2p-1) • (2p-1)

Which is the desired factorization

Multiplying Exponential Expressions:

3.4 Multiply (2p-1) by (2p-1)

The rule says : To multiply exponential expressions which have the same base, add up their exponents.

In our case, the common base is (2p-1) and the exponents are :

1 , as (2p-1) is the same number as (2p-1)1

and 1 , as (2p-1) is the same number as (2p-1)1

The product is therefore, (2p-1)(1+1) = (2p-1)2