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\(a,\left(3x+5\right)^2+\left(3x-5\right)^2-\left(3x+2\right)\left(3x-2\right)=9x^2+30x+25+9x^2-30x+25-9x^2+4=9x^2+54\)
\(b,BT=2x\left(4x^2-4x+1\right)-3x\left(x^2-9\right)-4x\left(x^2+2x+1\right)=8x^3-8x^2+2x-3x^3+27x-4x^3-8x^2-4x=x^3-16x^2+25x\)
\(c,BT=\left(x+y-z\right)^2-2\left(x+y-z\right)\left(x+y\right)+\left(x+y\right)^2=\left(x+y-z-x-y\right)^2=z^2\)
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TL:
\(\left(x+y\right)\left(x-y\right)\)
\(=x^2-xy+xy-y^2\)
\(=x^2-y^2\)
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a)
\(A=\left(x+3\right)\left(x^2-3x+9\right)-\left(54+x^3\right)\)
\(=x^3-3x^2+9x+3x^2-9x+27-54-x^3\)
\(=-27\)
or
\(A=x^3+27-54-x^3=-27\)
b)
\(B=\left(2x+y\right)\left(4x^2-2xy+y^2\right)-\left(2x-y\right)\left(4x^2+2xy+y^2\right)\)
\(=8x^3+y^3-8x^3+y^3=2y^3\)
c)
\(C=\left(2x+1\right)^2+\left(1-3x\right)^2+2\left(2x+1\right)\left(3x-1\right)\)
\(=\left(2x+1+3x-1\right)^2=\left(5x\right)^2=25x^2\)
d)
\(D=\left(x-2\right)\left(x^2+2x+4\right)-\left(x+1\right)^3+3\left(x-1\right)\left(x+1\right)\)
\(=x^3-8-\left(x-1\right)^3+3\left(x-1\right)\left(x+1\right)\)
\(=6x^2-3x-10\)
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\(2x\left(x-3y\right)-4y\left(x+2\right)-2\left(x^2-3y-4xy\right)\)
\(=2x^2-6xy-4xy+8y-2x^2-6y-8xy\)
\(=2x^2-10xy+8y-2x^2-14xy\)
\(=10xy+8y-14xy\)
\(=-4xy+8y\)
\(=-4.\left(\frac{-2}{3}.\frac{3}{4}\right)+8.\frac{3}{4}\)
\(=-4.\frac{-1}{2}+6\)
\(=2+6=8\)
\(2x^2-6xy-4xy-8y-2x^2+6y+8xy\)
\(=-2y-2xy\)
thay \(x=\frac{-2}{3};y=\frac{3}{4}\) vào biểu thức ta có
\(-2.\frac{3}{4}-2.\frac{-2}{3}\frac{3}{4}=\frac{-3}{2}+1=\frac{-3+2}{2}=\frac{-1}{2}\)
nếu có sai bn thông cảm
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2x\left(x-3y\right)-4y\left(x+2\right)-2\left(x^2-3y-4xy\right)\)
\(=2x^2-3y-4xy+8y-2x^2+3y+4xy\)
\(=-2y-2xy\)
Thay x,y ta có:
\(-2y-2xy=-2\left(\frac{3}{4}\right)-2\left(\frac{-2}{3}.\frac{3}{4}\right)\)
\(-2y-2xy=\frac{-3}{2}-2.\frac{-1}{2}\)
\(-2y-2xy=\frac{-3}{2}-\left(-1\right)\)
\(-2y-2xy=\frac{-3}{2}+1=\frac{-3}{2}+\frac{2}{2}=\frac{-1}{2}\)
Vậy biểu thức trên có giá trị bằng \(\frac{-1}{2}\)
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\(\left(x-y\right)^2-\left(x+y\right)^2=x^2-2xy+y^2-x^2-2xy-y^2\)
\(=-2xy-2xy=-4xy\)
\(\left(x-y\right)^2-\left(x+y\right)^2=\left(x-y-x-y\right)\left(x-y+x+y\right)=\left(-2y\right)\left(2x\right)=-4xy\)
(áp dụng hằng đẳng thức )