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\(\left(2x+3y\right)\left(2x-3y\right)-\left(2x-1\right)^2+\left(3y-1\right)^2\)
\(=4x^2-9y^2-4x^2+4x-1+9y^2-6y+1=4x-6y\)
Thay x = 1 ; y = -1 ta được :
\(4+6=10\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a. \(\left(2x^2+y\right)\left(2x^2-y\right)-4x^2+y^2=\left(2x^2\right)^2-y^2-4x^2+y^2\)
\(=4x^4-4x^2\)
b. \(\left(2x^2+y\right)^2-\left(2x^2-y^2\right)=4x^4+4x^2y+y^2-2x^2+y^2\)
\(=4x^4+4x^2y-2x^2+2y^2\)
c. \(\left(2x+1\right)\left(2x-1\right)-4x^2=\left(2x\right)^2-1^2-4x^2=4x^2-1-4x^2=-1\)
d. \(\left(2x^{3y}+y\right)^2-\left(y-2x^{3y}\right)^2\)
\(=\left(2x^{3y}+y+y-2x^{3y}\right)\left(2x^{3y}+y-y+2x^{3y}\right)\)
\(=2y.2.2x^{3y}=4y.2x^{3y}\)
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Đặt bthuc = A nhé
ĐKXĐ : \(2x\ne3y\)
\(A=\left[\dfrac{2x\left(4x^2+6xy+9y^2\right)}{\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)}-\dfrac{27y^3+36xy^2}{\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)}-\dfrac{24xy\left(2x-3y\right)}{\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)}\right]\left[\dfrac{2x\left(2x-3y\right)}{\left(2x-3y\right)}+\dfrac{9y^2+12xy}{\left(2x-3y\right)}\right]\)\(=\left[\dfrac{8x^3+12x^2y+18xy^2-27y^3-36xy^2-48x^2y+72xy^2}{\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)}\right]\left[\dfrac{4x^2-6xy+9y^2+12xy}{\left(2x-3y\right)}\right]\)
\(=\dfrac{8x^3-36x^2y+36xy^2-27y^3}{\left(2x-3y\right)\left(4x^2+6xy+9y^2\right)}\cdot\dfrac{4x^2+6xy+9y^2}{2x-3y}\)
\(=\dfrac{\left(2x-3y\right)^3}{\left(2x-3y\right)^2}=2x-3y\)
Với x = 1/3 ; y = -2 (tmđk) thay vào A ta được : A = 2.1/3 - 3.(-2) = 20/3
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(2x+3y)2+2(2x+3y)+1
= (2x+3y)(2x+3y+2+1)
= (2x+3y)(2x+3y+3)
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\(C=\left(2x+3y\right)\left(2x-3y\right)-\left(2x-1\right)^2+\left(3y-1\right)^2\)
\(C=4x^2-6xy+6xy-9y^2-4x^2+4x-1+9y^2-6y+1\)
\(C=4x-6y\)
Giá trị cảu biểu thức trên tại x=1 và y=-1 là:
\(C=4.1-6.\left(-1\right)=4+6=10\)
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a ) \(\left(3x-1\right)^2+\left(3x+1\right)^2+2\left(3x+1\right)\left(1-3x\right)\)
\(=\left(1-3x\right)^2+\left(3x+1\right)^2+2\left(3x+1\right)\left(1-3x\right)\)
\(=\left(1-3x+3x+1\right)^2\)
\(=2^2=4\)
b ) \(\left(2x-3y\right)^2+\left(2x+3y\right)^2+\left(2x-3y\right)\left(2x+3y\right)\)
\(=4x^2-12xy+9y^2+4x^2+12xy+9y^2+4x^2-9y^2\)
\(=\left(4x^2+4x^2+4x^2\right)+\left(9y^2+9y^2-9y^2\right)+\left(12xy-12xy\right)\)
\(=12x^2+9y^2\)