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Algebra II

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How do I solve the following problems??
1. Factor: 4x^2-100y^2

2. Factor: 3x^2+27

3. Solve 3x^2+9x=0

4. Solve 12^2+30x=-12

5. 9a(a+1)=4

6. Solve 16x^2=25

  • Algebra II -

    Hints:

    1. Factor: 4x^2-100y^2
    use difference of two squares,
    (a²-b²)=(a+b)(a-b)

    2. Factor: 3x^2+27
    the common factor is 3.

    3. Solve 3x^2+9x=0
    factor and solve:
    3x(x+3)=0
    therefore
    x=0 or x=?

    4. Solve 12^2+30x=-12
    Factor out the 6, and then factor completely to solve for x:
    6(2x²+5x+2)=0
    Hint: it's in the form
    (2x 1)(x 2)

    5. 9a(a+1)=4
    Expand, transpose everything to the left, and then factor.
    9a²+9a-4=0

    6. Solve 16x^2=25
    isolate variable:
    x²=(25/16)=(5/4)²
    and solve for x.

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