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a: Sửa đề: y=2/3
\(P=\left(3y+\dfrac{1}{3}\right)^3=\left(3\cdot\dfrac{2}{3}+\dfrac{1}{3}\right)^3=\left(\dfrac{7}{3}\right)^3=\dfrac{343}{27}\)
b: \(Q=x^2+4xy+4y^2-2x-4y+10\)
\(=\left(x+2y\right)^2-2\left(x+2y\right)+10\)
\(=5^2-2\cdot5+10=25\)
a: Sửa đề: \(P=27y^3+9y^2+y+\dfrac{1}{27}\)
\(=\left(3y+\dfrac{1}{3}\right)^3\)
\(=\left(3\cdot\dfrac{2}{3}+\dfrac{1}{3}\right)^3=\left(\dfrac{7}{3}\right)^3=\dfrac{343}{27}\)
b: \(Q=x^2+4xy+4y^2-2x-4y+10\)
\(=\left(x+2y\right)^2-2\left(x+2y\right)+10\)
\(=25-2\cdot5+10=25\)
a: \(P=\left(3y+\dfrac{1}{3}\right)^3=\left(3\cdot\dfrac{2}{3}+\dfrac{1}{3}\right)^3=\left(\dfrac{7}{3}\right)^3=\dfrac{343}{27}\)
b: \(Q=x^2+4xy+4y^2-2\left(x+2y\right)+10\)
\(=\left(x+2y\right)^2-2\left(x+2y\right)+10\)
=25
\(P=27y^3+9y^2+y+\dfrac{1}{27}=\left(3y+3\right)^3\)
Với \(y=\dfrac{2}{3}\) ta có:
\(P=\left(3.\dfrac{2}{3}+3\right)^3=5^3=125\)
\(Q=x^2+4y^2-2x+10+4xy-4y\)
\(=\left(x^2-2x+4xy\right)+4y^2-4y+10\)
\(=\left[x^2-2x\left(1-2y\right)+\left(1-2y\right)^2\right]+4y^2-4y+10-\left(1-2y\right)^2\)\(=\left(x+2y-1\right)^2+4y^2-4y+10-1+4y-4y^2\)\(=\left(x+2y-1\right)^2+9\)
Với \(x+2y=5\) , ta có:
\(Q=\left(5-1\right)^2+9=25\)
a) \(\left(x+\dfrac{1}{2}\right)^2-2x^2\)
\(=x^2+2\cdot x\cdot\dfrac{1}{2}+\left(\dfrac{1}{2}\right)^2-2x^2\)
\(=x^2+x+\dfrac{1}{4}-2x^2\)
\(=-x^2+x+\dfrac{1}{4}\)
b) \(\left(x-2y\right)^2-4y^2\)
\(=x^2-2\cdot x\cdot2y+\left(2y\right)^2-4y^2\)
\(=x^2-4xy+4y^2-4y^2\)
\(=x^2-4xy\)
c) \(\left(x+\dfrac{1}{2}y\right)^3\)
\(=x^3+3\cdot x^2\cdot\dfrac{1}{2}y+3\cdot x+\left(\dfrac{1}{2}y\right)^2+\left(\dfrac{1}{2}y\right)^3\)
\(=x^3+\dfrac{3}{2}x^2y+\dfrac{3}{4}xy^2+\dfrac{1}{8}y^3\)
d) \(\left(2x^2-3y\right)^3\)
\(=\left(2x^2\right)^3-3\cdot\left(2x^2\right)^2\cdot3y+3\cdot2x^2\cdot\left(3y\right)^2-\left(3y\right)^3\)
\(=8x^6-36x^4y+54x^2y^2-27y^3\)
e) \(\left(x^2+y\right)^2-\left(x+y\right)^2\)
\(=\left[\left(x^2\right)^2+2\cdot x^2\cdot y+y^2\right]-\left(x^2+2\cdot x\cdot y+y^2\right)\)
\(=\left(x^4+2x^2y+y^2\right)-\left(x^2+2xy+y^2\right)\)
\(=x^4+2x^2y+y^2-x^2-2xy-y^2\)
\(=x^4+2x^2y-x^2-2xy\)
-(a - 3)2 = -(a2 - 6a + 9) = -a2 + 6a - 9
(x - 2)(x + 2) = x2 - 4
-(5 + 4y)(5 - 4y) = -(25 - 16y2) = -25 + 16y2
(\(\dfrac{1}{2}\)x + 2y)(\(\dfrac{1}{2}\)x - 2y) = \(\dfrac{1}{4}\)x2 - 4y2