What is the complete factorization of 4x2 – 24xy + 36y2 ?

The complete factorization of are 4(x-3y)(x+3y)

Solution:

Given Data:

Take common value in all the three term.so we take 4 as common term in the above expression

Now factorize the expression

Find the two numbers, whose product should be 9 and sum should be -6.

-3,-3 are the numbers which satisfy the above condition.

When we add -3-3=Sum is 6

Product of -3 -3= 9  

-3 , -3 satisfies the condition.

So the expression will become as =

Take the common term

x(x-3y)+3y(x-3y)  

(x-3y)(x+3y)  

hence the complete factorization of are 4(x-3y)(x+3y)

215.92 dollars is the answer

(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