Perfect square trinomial conditions

Step-by-step explanation:

step 1. an example of difference of squares (dos) is (x + y)(x - y) = x^2 - y^2.

step 2. dos must have only 2 square rootable terms and a "-" between them.

step 3. 196x^2 - 121y^2 = (14x + 11y)(14x - 11y) works!

step 4. 5x^2 - 245 = 5(x^2 - 49) = 5(x + 7)(x - 7) works!

step 5. 27w^5 - 75w = 3w(9w^4 - 25) = 3w(3w^2 + 5)(3w^2 - 5) works!

step 6. x^4 - 100y^2 = (x^2 - 10y)(x^2 + 10y) works!

c.

step-by-step explanation:

because first you have to add the 4x, 9x, and the 7x together and you get 20x and then you add the last numbers up and you get 5and then you put the subtraction sign in there and that's how you get the answer.

simplifying

5(x + -6) = 2(x + 3)

reorder the terms:

5(-6 + x) = 2(x + 3)

(-6 * 5 + x * 5) = 2(x + 3)

(-30 + 5x) = 2(x + 3)

reorder the terms:

-30 + 5x = 2(3 + x)

-30 + 5x = (3 * 2 + x * 2)

-30 + 5x = (6 + 2x)

solving

-30 + 5x = 6 + 2x

solving for variable 'x'.

move all terms containing x to the left, all other terms to the right.

add '-2x' to each side of the equation.

-30 + 5x + -2x = 6 + 2x + -2x

combine like terms: 5x + -2x = 3x

-30 + 3x = 6 + 2x + -2x

combine like terms: 2x + -2x = 0

-30 + 3x = 6 + 0

-30 + 3x = 6

add '30' to each side of the equation.

-30 + 30 + 3x = 6 + 30

combine like terms: -30 + 30 = 0

0 + 3x = 6 + 30

3x = 6 + 30

combine like terms: 6 + 30 = 36

3x = 36

divide each side by '3'.

x = 12

simplifying

x = 12

this should .