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a/ \(\left(2x+1\right)\left(2x-1\right)-4x^2=\left(2x\right)^2-1^2-4x^2\)
\(=4x^2-1-4x^2\)
b/ \(\left(2x^2+y\right)\left(2x^2-y\right)-4x^2+y^2\)
\(=\left(2x^2\right)^2-y^2-4x^2+y^2=4x^4-y^2-4x^2+y^2=4x^4-4x^2\)
c/ \(\left(2x^2+y\right)^2-\left(2x^2-y\right)^2\)
\(=\left(2x^2+y+2x^2-y\right)\left(2x^2+y-2x^2+y\right)\)
\(=4x^2\cdot2y=8x^2y\)
d/ \(\left(2x^3y+y\right)^2-\left(y-2x^3y\right)^2=\left(2x^3y+y\right)^2-\left(2x^3y-y\right)^2\)
\(=\left(2x^3y+y+2x^3y-y\right)\left(2x^3y+y-2x^3y+y\right)\)
\(=4x^3y\cdot2y=8x^3y^2\)
a: \(\left(x+2\right)^2=x^2+2\cdot x\cdot2+2^2=x^2+4x+4\)
b: \(\left(2x+y\right)^2=\left(2x\right)^2+2\cdot2x\cdot y+y^2=4x^2+4xy+y^2\)
c: \(\left(x-3y\right)^2=x^2-2\cdot x\cdot3y+\left(3y\right)^2=x^2-6xy+9y^2\)
d: \(\left(\dfrac{1}{2}x-y\right)^2=\left(\dfrac{1}{2}x\right)^2-2\cdot\dfrac{1}{2}x\cdot y+y^2\)
\(=\dfrac{1}{4}x^2-xy+y^2\)
e: \(\left(x^2-y\right)^2=\left(x^2\right)^2-2\cdot x^2y+y^2=x^4-2x^2y+y^2\)
a) \(\left(x+2\right)^2\)
\(=x^2+2\cdot x\cdot2+2^2\)
\(=x^2+4x+4\)
b) \(\left(2x+y\right)^2\)
\(=\left(2x\right)^2+2\cdot2x\cdot y+y^2\)
\(=4x^2+4xy+y^2\)
c) \(\left(x-3y\right)^2\)
\(=x^2-2\cdot x\cdot3y+\left(3y\right)^2\)
\(=x^2-6xy+9y^2\)
d) \(\left(\dfrac{1}{2}x-y\right)^2\)
\(=\left(\dfrac{1}{2}x\right)^2-2\cdot\dfrac{1}{2}x\cdot y+y^2\)
\(=\dfrac{x^2}{4}-xy+y^2\)
e) \(\left(x^2-y\right)^2\)
\(=\left(x^2\right)^2-2\cdot x^2\cdot y+y^2\)
\(=x^4-2x^2y+y^2\)
\(2x^3y-2xy^3-4xy^2-2xy\)
\(=2xy.\left(x^2-y^2-2y-1\right)\)
\(=2xy.[x^2-\left(y^2+2y+1\right)]\)
\(=2xy.[x^2-\left(y+1\right)^2]\)
\(=2xy.\left(x+y+1\right).\left(x-y-1\right)\)
Vậy chọn đáp án A
a) (x-y)(2x+3y)=2x2+3xy-2xy+3y2=2x2+xy+3y2
b) (2x-1)2-(2x-1)=0
<=> 2x-1=0 <=> x=\(\dfrac{1}{2}\)
a) Ta có: (x-y)(2x+3y)
\(=2x^2+3xy-2xy-3y^2\)
\(=2x^2+xy-3y^2\)
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. \(\left(2x^{3y}+y\right)^2-\left(y-2x^{3y}\right)^2\)
\(=\left(2x^{3y}+y+y-2x^{3y}\right)\left(2x^{3y}+y-y+2x^{3y}\right)\)
\(=2y.2.2x^{3y}=4y.2x^{3y}\)