Answer:

1. (y-10)²

Step-by-step explanation:

The first term is, y2 its coefficient is 1 .

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

The last term, "the constant", is +100

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

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

y2 - 10y - 10y - 100

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

y • (y-10)

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

10 • (y-10)

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

(y-10) • (y-10)

Which is the desired factorization

Multiplying Exponential Expressions:

1.2 Multiply (y-10) by (y-10)

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

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

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

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

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