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16x^{2}-8x+1-\left(3x+4\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4x-1\right)^{2}.
16x^{2}-8x+1-\left(9x^{2}+24x+16\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+4\right)^{2}.
16x^{2}-8x+1-9x^{2}-24x-16
To find the opposite of 9x^{2}+24x+16, find the opposite of each term.
7x^{2}-8x+1-24x-16
Combine 16x^{2} and -9x^{2} to get 7x^{2}.
7x^{2}-32x+1-16
Combine -8x and -24x to get -32x.
7x^{2}-32x-15
Subtract 16 from 1 to get -15.
16x^{2}-8x+1-\left(3x+4\right)^{2}
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(4x-1\right)^{2}.
16x^{2}-8x+1-\left(9x^{2}+24x+16\right)
Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(3x+4\right)^{2}.
16x^{2}-8x+1-9x^{2}-24x-16
To find the opposite of 9x^{2}+24x+16, find the opposite of each term.
7x^{2}-8x+1-24x-16
Combine 16x^{2} and -9x^{2} to get 7x^{2}.
7x^{2}-32x+1-16
Combine -8x and -24x to get -32x.
7x^{2}-32x-15
Subtract 16 from 1 to get -15.