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\(27x^3+125y^3\)
\(=\left(3x\right)^3+\left(5y\right)^3\)
\(=\left(3x+5y\right)\left(9x^2-15xy+25y^2\right)\)
\(16x^2-24xy+9y^2\)
\(=\left(4x\right)^2-2.4x.3y+\left(3y\right)^2\)
\(=\left(4x-3y\right)^2\)
(X-y-4)2-(2x+3y-1)2
=(X-Y-4-2X-3Y+1)(X-Y-4+2X+3Y-1)=(-X-4Y-3)(X+2Y-5)
(2x2+1)2+6(2x2+1)+9
=(2X2+1+3)2 (dùng hằng đẳng thức a2 +2ab+b2 =(a+b)2
=(2x2+4)2=(2(x2+2))2=4(x2+2)2
\(a,\left(x-y-4\right)^2-\left(2x+3y-1\right)^2\)
\(=\left(3x-2y-5\right)\left(-x-4y-3\right)\)
\(b,\left(2x^2+1\right)^2+6\left(2x^2+1\right)+9\)
\(=\left(2x^2+4\right)^2\)
\(ax+bx+ay+by\)
\(=x\left(a+b\right)+y\left(a+b\right)\)
\(=\left(x+y\right)\left(a+b\right)\)
\(xy+1-x-y\)
\(=x\left(y-1\right)-\left(y-1\right)\)
\(=\left(x-1\right)\left(y-1\right)\)
1/(x+2)2 -(3x-1)2=(x+2+3x-1)(x+2-3x+1)=4x(-2x+3)=-8x2+12x
2/(x4+x2)(-2x3-2x)=x2(x2+1)-2x(x2+1)=(x2+1)(x2-2x)
\(-3x^2+4x-2020\)
\(=-3\left(x^2-\frac{4}{3}x+\frac{2020}{3}\right)\)
\(=-3\left(x^2-\frac{4}{3}x+\frac{4}{9}+\frac{6056}{9}\right)\)
\(=-3\left[\left(x-\frac{2}{3}\right)^2+\frac{6056}{9}\right]\)
\(=-3\left(x-\frac{2}{3}\right)^2-\frac{6056}{3}\ge-\frac{6056}{3}\)
(Dấu "=" \(\Leftrightarrow x-\frac{2}{3}=0\Leftrightarrow x=\frac{2}{3}\))
a)\(=\left(x-2\right)\left(5x-3x^2\right)\)
\(=x\left(x-2\right)\left(5-3x\right)\)
b)\(=\left(4x-x^2-4\right)\left(4x+x^2+4\right)\)
\(=-\left(x^2-4x+4\right)\left(x+2\right)^2\)
=\(-\left(x-2\right)^2\left(x+2\right)^2\)
c)\(\left(=5x^2-5xy\right)+\left(7y-7x\right)\)
\(=-5x\left(y-x\right)+7\left(y-x\right)\)
\(=\left(y-x\right)\left(7-5x\right)\)
d)\(=\left(3x^2-6x\right)-\left(2x-4\right)\)
\(=3x\left(x-2\right)-2\left(x-2\right)\)
\(=\left(x-2\right)\left(3x-2\right)\)
e)\(=[\left(x^2\right)^2+8^2+2.x^2.8]-2.8.x^2\)
\(=\left(x^2+8\right)^2-16x^2\)
\(=\left(x^2+8-4x\right)\left(x^2+8+4x\right)\)
__Chúc bạn hc tốt ......
\(36x^2-\left(3x-2\right)^2\)
\(=\left(6x\right)^2-\left(3x-2\right)^2\)
\(=\left(6x+3x-2\right)\left(6x-3x+2\right)\)
\(=\left(9x-2\right)\left(3x+2\right)\)
\(-49x^2+9\)
\(=3^2-\left(7x\right)^2\)
\(=\left(3-7x\right)\left(3+7x\right)\)