Write the square of the binomial as a polynomial: (-1 1/3p + 6q)^2

p² -16pq + 36q²

Step-by-step explanation:

Given

(- p + 6q)²

= (- p + 6q)(- p + 6q)

Each term in the second factor is multiplied by each term in the first factor, that is

- p(- p + 6q) + 6q(- p + 6q)

= p² - 8pq - 8pq + 36q² ← collect like terms

= p² - 16pq + 36q²

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240