Question

factorise =100p²_20p+1​

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

((22•52p2) - 20p) + 1

STEP

2

:

Trying to factor by splitting the middle term

2.1 Factoring 100p2-20p+1

The first term is, 100p2 its coefficient is 100 .

The middle term is, -20p its coefficient is -20 .

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

Step-1 : Multiply the coefficient of the first term by the constant 100 • 1 = 100

Step-2 : Find two factors of 100 whose sum equals the coefficient of the middle term, which is -20 .

-100 + -1 = -101

-50 + -2 = -52

-25 + -4 = -29

-20 + -5 = -25

-10 + -10 = -20 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -10 and -10

100p2 - 10p - 10p - 1

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

10p • (10p-1)

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

1 • (10p-1)

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

(10p-1) • (10p-1)

Which is the desired factorization

Multiplying Exponential Expressions:

2.2 Multiply (10p-1) by (10p-1)

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

In our case, the common base is (10p-1) and the exponents are :

1 , as (10p-1) is the same number as (10p-1)1

and 1 , as (10p-1) is the same number as (10p-1)1

The product is therefore, (10p-1)(1+1) = (10p-1)2

Final result :

(10p - 1)2

Step-by-step explanation:

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