Need help on Algebra 1 hw?

I can't figure out how to solve for p, 3x^p(4x^{2p+3}+2x^{3p-2})=12x^{12}+6x^{10}

1 Answer
R. Nguyen
Jan 30, 2018

p = 3

Explanation:

color(red)(3x^p)(4x^{2p+3}+2x^{3p-2})=12x^{12}+6x^{10}

First, we might want to expand out our left-hand side.

color(red)(3x^p)*4x^{2p+3}+color(red)(3x^p)*2x^{3p-2}=12x^{12}+6x^{10}

Recall that x^a*x^b=x^{a+b}.

(color(red)3 * 4)x^{color(red)p + 2p + 3} + (color(red)3 * 2)x^{color(red)p + 3p - 2} = 12x^{12}+6x^{10}

12x^{color(blue)(3p + 3)} + 6x^{color(blue)(4p - 2)} = 12x^{color(blue)12}+6x^{color(blue)10}

Doing a little bit of pattern matching, we notice that color(blue)(3p + 3) corresponds exactly to color(blue)12, and that color(blue)(4p-2) corresponds exactly to color(blue)(10). This means that they must be equal.

3p + 3 = 12

4p - 2 = 10

Solving either of these equations tells us that p = 3.

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