Evaluate
4\left(c-2x\right)\left(x+3c\right)
Expand
12c^{2}-20cx-8x^{2}
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16c^{2}-8cx+x^{2}-\left(2c+3x\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4c-x\right)^{2}.
16c^{2}-8cx+x^{2}-\left(4c^{2}+12cx+9x^{2}\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2c+3x\right)^{2}.
16c^{2}-8cx+x^{2}-4c^{2}-12cx-9x^{2}
To find the opposite of 4c^{2}+12cx+9x^{2}, find the opposite of each term.
12c^{2}-8cx+x^{2}-12cx-9x^{2}
Combine 16c^{2} and -4c^{2} to get 12c^{2}.
12c^{2}-20cx+x^{2}-9x^{2}
Combine -8cx and -12cx to get -20cx.
12c^{2}-20cx-8x^{2}
Combine x^{2} and -9x^{2} to get -8x^{2}.
16c^{2}-8cx+x^{2}-\left(2c+3x\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4c-x\right)^{2}.
16c^{2}-8cx+x^{2}-\left(4c^{2}+12cx+9x^{2}\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(2c+3x\right)^{2}.
16c^{2}-8cx+x^{2}-4c^{2}-12cx-9x^{2}
To find the opposite of 4c^{2}+12cx+9x^{2}, find the opposite of each term.
12c^{2}-8cx+x^{2}-12cx-9x^{2}
Combine 16c^{2} and -4c^{2} to get 12c^{2}.
12c^{2}-20cx+x^{2}-9x^{2}
Combine -8cx and -12cx to get -20cx.
12c^{2}-20cx-8x^{2}
Combine x^{2} and -9x^{2} to get -8x^{2}.
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