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1)a)=>x2+y2+2xy-4(x2-y2-2xy)
=>x2+y2+2xy-4.x2+4y2+8xy
=>-3.x2+5y2+10xy
\(\frac{x+3}{x^2-4}.\frac{8-12x+6x^2-x^3}{9x+27}\)
\(=\frac{\left(x+3\right)\left(2-x\right)^3}{\left(x+2\right)\left(x-2\right).9\left(x+3\right)}\)
\(=-\frac{\left(x-2\right)^2}{9\left(x+2\right)}\)
a: ĐKXĐ: x<>-3
b: \(Q=\left(\dfrac{x}{x^2-3x+9}-\dfrac{11}{\left(x+3\right)\left(x^2-3x+9\right)}+\dfrac{1}{x+3}\right)\cdot\dfrac{x+3}{x^2-1}\)
\(=\dfrac{x^2+3x-11+x^2-3x+9}{\left(x+3\right)\left(x^2-3x+9\right)}\cdot\dfrac{x+3}{x^2-1}\)
\(=\dfrac{2x^2-2}{x^2-1}\cdot\dfrac{1}{x^2-3x+9}=\dfrac{2}{x^2-3x+9}\)
a: \(\left(3x+2\right)^2+4x-3x^2+2\left(5x-2\right)\left(5x+2\right)-75x^2\)
\(=9x^2+12x+4+4x-3x^2+50x^2-8-75x^2\)
\(=-19x^2+16x-4\)
\(a,\)\(2\left(x-y\right)\left(x+y\right)+\left(x-y\right)^2+\left(x+y\right)^2.\)
\(=\left[\left(x-y\right)+\left(x+y\right)\right]^2=\left(x-y+x+y\right)^2=x^2\)
\(b,\)\(\left(2x-3\right)\left(4x^2+6x+9\right)-\left(54+8x\right)\)
\(=8x^2-27-54-8x=8x^2-8x-81\)
\(c,\)\(\left(3x+y\right)\left(9x^2-3xy+y^2\right)-\left(3x-y\right)\left(9x^2+3xy+y^2\right)\)
\(=27x^3+y^3-\left(27x^3-y^3\right)=2y^3\)
\(d,\)\(\left(a+b+c\right)^2-\left(a-c\right)^2-2ab+2bc\)
\(=a^2+b^2+c^2+2ab+2bc+2ac-a^2+2ac-c^2-2ab+2bc\)
\(=b^2+4bc+4ac\)
\(\frac{x+3}{x^2-4}.\frac{8-12x+6^2-x^3}{9x+27}\)
\(=\frac{x+3}{x^2-4}.\frac{-x^3+6x^2-4}{9x+27}\)
\(=\frac{\left(x+3\right)\left(-x^3+6x^2-4\right)}{\left(x^2-4\right)\left(9x+27\right)}\)
\(=\frac{\left(x+3\right)\left(-x^3+6x-4\right)}{9\left(x+3\right)\left(x^2-4\right)}\)
\(=\frac{-x^3+6x^2-4}{9\left(x^2-4\right)}\)
Mk ko chắc
(x+3 )/ (x-2)(x+2) . [(2-x)^3 / 9(x+3)]
= -(x-2)^2 / [(x+2).9]