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Bài 1:
a) \(-5\left(x^2-3x+1\right)+x\left(1+5x\right)=x-2\)
\(\Rightarrow-5x^2+15x-5+x+5x^2=x-2\)
\(\Rightarrow16x-5=x-2\)
\(\Rightarrow16x-x=5-2\)
\(\Rightarrow15x=3\)
\(\Rightarrow x=\dfrac{15}{3}=5\)
b) \(12x^2-4x\left(3x+5\right)=10x-17\)
\(\Rightarrow12x^2-12x^2-20x=10x-17\)
\(\Rightarrow-20x=10x-17\)
\(\Rightarrow-20x-10x=-17\)
\(\Rightarrow-30x=-17\)
\(\Rightarrow x=\dfrac{-30}{-17}=\dfrac{30}{17}\)
c) \(-4x\left(x-5\right)+7x\left(x-4\right)-3x^2=12\)
\(\Rightarrow-4x^2+20x+7x^2-28x-3x^2=12\)
\(\Rightarrow-8x=12\)
\(\Rightarrow x=\dfrac{12}{-8}=-\dfrac{4}{3}\)
Bài 2:
a) \(\left(x+5\right)\left(x-7\right)-7x\left(x-3\right)\)
\(=x^2-7x+5x-35-7x^2+21x\)
\(=-6x^2+19x-35\)
b) \(x\left(x^2-x-2\right)-\left(x-5\right)\left(x+1\right)\)
\(=x^3-x^2-2x-x^2+x-5x-5\)
\(=x^3-2x^2-6x-5\)
c) \(\left(x-5\right)\left(x-7\right)-\left(x+4\right)\left(x-3\right)\)
\(=x^2-7x-5x+35-x^2-3x+4x-12\)
\(=11x+23\)
d) \(\left(x-1\right)\left(x-2\right)-\left(x+5\right)\left(x+2\right)\)
\(=x^2-2x-x+2-x^2+2x+5x+10\)
\(=4x+12\)
\(a,-3x^2+7x-9+\left(x-1\right)\left(x+2\right)\\ =-3x^2+7x-9+x^2-x+2x-2\\ =\left(-3x^2+x^2\right)+\left(7x-x+2x\right)-\left(9+2\right)\\ =-2x^2+8x-11\\ b,x\left(x-5\right)-2x\left(x+1\right)\\ =x^2-5x-2x^2-2x\\ =\left(x^2-2x^2\right)-\left(5x+2x\right)\\ =-3x^2-7x\\ c,4x\left(x^2-x+1\right)-\left(x-1\right)\left(x^2-x\right)\\ =4x^3-4x^2+4x-x\left(x^2-x\right)+x^2-x\\ =4x^3-4x^2+4x-x^3+x^2+x^2-x\\ =\left(4x^3-x^3\right)+\left(-4x^2+x^2+x^2\right)+\left(4x-x\right)\\ =3x^3-2x^2+3x\\ =x\left(3x^2-2x+3\right)\)
\(d,-5x\left(x-5\right)+\left(x-3\right)\left(x^2-7\right)\\ =-5x^2+25x+x\left(x^2-7\right)-3\left(x^2-7\right)\\ =-5x^2+25x+x^3-7x-3x^2+21\\ =\left(-5x^2-3x^2\right)+\left(25x-7x\right)+x^3+21\\ =-8x^2+x^3+18x+21\)
Ta có: \(B=\left|x-\dfrac{1}{7}\right|-\left|x+\dfrac{3}{5}\right|+\dfrac{4}{5}\)
\(=-x+\dfrac{1}{7}-x-\dfrac{3}{5}+\dfrac{4}{5}\)
\(=-2x+\dfrac{12}{35}\)
A=(x-5)(x+7)-7x(x+3)
\(=x^2+7x-5x-35-7x^2-21x\)
\(=-6x^2-19x-35\)
(x - 5)(x + 7) - 7x(x + 3)
= x² + 7x - 5x - 35 - 7x² - 21x
= (x² - 7x²) + (7x - 5x - 21x) - 35
= -6x² - 19x - 35