a. \(A=\left(4-5x\right)^2-\left(3+5x\right)^2\\ =\left(4-5x+3+5x\right)\left(4-5x-3-5x\right)\\ =7.\left(-5x\right)=-35x\)
b. \(B=\left(3x-1\right)\left(1+3x\right)-\left(3x+1\right)^2\\ =9x^2-1-\left(9x^2+6x+1\right)\\ =9x^2-1-9x^2-6x-1\\ =-6x-2\)
a) Ta có: \(A=\left(4-5x\right)^2-\left(5x+3\right)^2\)
\(=\left(4-5x-5x-3\right)\left(4-5x+5x+3\right)\)
\(=7\left(-10x+1\right)\)
\(=-70x+7\)
b) Ta có: \(B=\left(3x-1\right)\left(3x+1\right)-\left(3x+1\right)^2\)
\(=\left(3x+1\right)\left(3x-1-3x-1\right)\)
\(=-2\left(3x+1\right)\)
\(=-6x-2\)
c) Ta có: \(C=\left(2x+5\right)^3-\left(2x-5\right)^3-\left(120x^2+49\right)\)
\(=8x^3+60x^2+150x+125-\left(8x^3-60x^2+150x-125\right)-120x^2-49\)
\(=8x^3-60x^2+150x+76-8x^3+60x^2-150x+125\)
\(=201\)
e) Ta có: \(E=4\cdot\left(5+1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)-5^{16}\)
\(=\left(5-1\right)\left(5+1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)-5^{16}\)
\(=\left(5^2-1\right)\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)-5^{16}\)
\(=\left(5^4-1\right)\left(5^4+1\right)\left(5^8+1\right)-5^{16}\)
\(=\left(5^8-1\right)\left(5^8+1\right)-5^{16}\)
\(=5^{16}-1-5^{16}\)
=-1
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