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1:
a: \(\left(2x-5\right)^2-4x\left(x+3\right)\)
\(=4x^2-20x+25-4x^2-12x\)
=-32x+25
b: \(\left(x-2\right)^3-6\left(x+4\right)\left(x-4\right)-\left(x-2\right)\left(x^2+2x+4\right)\)
\(=x^3-6x^2+12x-8-\left(x^3-8\right)-6\left(x^2-16\right)\)
\(=-6x^2+12x-6x^2+96=-12x^2+12x+96\)
c: \(\left(x-1\right)^2-2\left(x-1\right)\left(x+2\right)+\left(x+2\right)^2+5\left(2x-3\right)\)
\(=\left(x-1-x-2\right)^2+5\left(2x-3\right)\)
\(=\left(-3\right)^2+5\left(2x-3\right)\)
\(=9+10x-15=10x-6\)
2:
a: \(\left(2-3x\right)^2-5x\left(x-4\right)+4\left(x-1\right)\)
\(=9x^2-12x+4-5x^2+20x+4x-4\)
\(=4x^2+12x\)
b: \(\left(3-x\right)\left(x^2+3x+9\right)+\left(x-3\right)^3\)
\(=27-x^3+x^3-9x^2+27x-27\)
\(=-9x^2+27x\)
c: \(\left(x-4\right)^2\left(x+4\right)-\left(x-4\right)\left(x+4\right)^2+3\left(x^2-16\right)\)
\(=\left(x-4\right)\left(x+4\right)\left(x-4-x-4\right)+3\left(x^2-16\right)\)
\(=\left(x^2-16\right)\left(-8\right)+3\left(x^2-16\right)\)
\(=-5\left(x^2-16\right)=-5x^2+80\)
a) \(\left(x-3\right)\left(3x+2\right)-3x\left(x-5\right)+3\)
\(=x.\left(3x+2\right)-3.\left(3x+2\right)-3x\left(x-5\right)+3\)
\(=x.3x+x.2-3.3x-3.2-3x.x+3x.5+3\)
\(=3x^2+2x-9x-6-3x^2+15x+3\)
\(=8x-3\)
b )
\(2x\left(x-3\right)-\left(x-5\right)\left(2x-1\right)\)
\(2x.x-2x.3-x.\left(2x-1\right)-5.\left(2x-1\right)\)
\(2x.x-2x.3-x.2x+x.1-5.2x+5.x\)
\(2x^3-6x-2x^2+x-10x+5x\)
\(2x^3-15x-2x^2\)
\(a,=x^2+6x+9+2x^2+5xy^2=3x^2+6x+5xy^2+9\\ b,=9x^2-12x+4-9x^2+1=-12x+5\)
Bạn đăng từng bài 1 và tách bài ra cho dễ nhìn hơn nhé!
3A:
a: =15x^4-5x^2-24x^4+18x^2-6x-6x^4+2x^3
=-15x^4+2x^3+13x^2-6x
b: =1/2(x^3-2/5x^2+2x)-3/4x^3-1/4x^2-x^2-x
=1/2x^3-1/5x^2+x-3/4x^3-5/4x^2-x
=-1/4x^3-29/20x^2
c: =3/2x^2(x^2-2x)-2x(x^3+x^2+1)+2(x-1)
=3/2x^4-3x^3-2x^4-2x^3-2x+2x-2
=-1/2x^4-5x^3-2
d: =x^4-2x^3+5x^3-10x^2+5/2x-x^4+x^3-x^2
=4x^3-11x^2+5/2x
a: Ta có: \(\left(x+5\right)^2-4x\left(2x+3\right)^2-\left(2x-1\right)\left(x+3\right)\left(x-3\right)\)
\(=x^2+10x+25-4x\left(4x^2+12x+9\right)-\left(2x-1\right)\left(x^2-9\right)\)
\(=x^2+10x+25-16x^3-48x^2-36x-2x^3+18x+x^2-9\)
\(=-18x^3-46x^2-8x+16\)
a: \(\left(x+1\right)^3+\left(x-2\right)^3=2x^3+2\left(2x-1\right)^2-9\)
\(\Leftrightarrow x^3+3x^2+3x+1+x^3-6x^2+12x-8=2x^3+2\left(4x^2-4x+1\right)-9\)
\(\Leftrightarrow2x^3-3x^2+15x-7=2x^3+8x^2-8x-7\)
\(\Leftrightarrow-11x^2+23x=0\)
\(\Leftrightarrow x\left(-11x+23\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=\dfrac{23}{11}\end{matrix}\right.\)
Bài 2:
a: Ta có: \(A=\left(x+1\right)^3+\left(x-1\right)^3\)
\(=x^3+3x^2+3x+1+x^3-3x^2+3x-1\)
\(=2x^3+6x\)
b: Ta có: \(B=\left(x-3\right)^3-\left(x+3\right)\left(x^2-3x+9\right)+\left(3x-1\right)\left(3x+1\right)\)
\(=x^3-9x^2+27x-27-x^3-27+9x^2-1\)
\(=27x-55\)
