Completing the square

Question

Complete the square with (y^2-9y) to get three terms

Answer 1

y^4 - 18y^3 +81y^2

maybe you can see that better if you factor out a y first

y(y-9) then square each factor

y^2 and

y^2 -18y + 81

then multiply those two products together

y^2(y^2-18y+81) = y^4-18y^3+81y^2

another method:

to square two terms, square each term, the y^2 and -9y,

then double the product of the the two terms 2(-9y^3) = -18y^3

another way of looking at the problem

is write it as (y^2-9y)(y^2-9y) then use the FOIL method

y^2 times y^2, get the product of the first terms: "F" is for first

Then take the product of the outer terms "O" is for outer

that's y^2 times -9y = -9y^3

then take the product of the inner terms:

-9y times y^2 = another -9y^3

add the inner and outer products to get -18y^3

then last, multiply the last term in each factor

-9y times -9y = +81y

Put them all together FOIL

y^4 -18y^3 + 81y^2

Answer 2

You can find the c term using the formula (b/2)²

The b term is -9

Plugging this in:

c = (-9/2)² = 81/4

y²-9y+81/4

Factored form: (y-9/2)(y-9/2) = (y-9/2)²