HELP! Algebra. DONT UNDERSTAND

Factor each of the following expressions completely and then simplify, if possible:
a: ax + 2x
b: ax - 2x
c: 3x - 4x + 7x
d: 3x^2 + xy - x
e: (a + b)(c + 1) - (a + b)
f: x^2 - 9y^2
g: (x^2 - y^2) + x + y

asked by KG
  1. A: x(a+2)

    posted by Kim
  2. a: ax+2x = x(a+2)
    b: ax-2x = x(a-2)
    c: 3x-4x+7x = x(3-4+7) = 6x
    d: 3x^2+xy-x = x(3x+y-1)
    e: (a+b)(c+1)-(a+b) = ac+bc = c(a+b)
    f: x^2-9y^2 = x=3y
    g:(x^2 - y^2) + x + y = y-x

    posted by niezel
  3. How did you do this??

    posted by KG
  4. Niezel is correct from a - e

    explanation of e)
    (a+b)(c+1)-(a+b) = ac+bc = c(a+b)
    by common factor of (a_+b)
    = (a+b)(c+1 - 1)
    = c(a+b)

    f)
    x^2 - 9y^2 ----- standard difference of squares
    = (x+3y)(x-3y)

    g)
    (x^2 - y^2) + x + y
    = (x-y)(x+y) + (x+y) , difference of squares at the front, no damage done by putting in brackets at the end
    = (x+y)(x-y + 1) --- just used a common factor of (x+y)

    posted by Reiny

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