Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
a, \(\left(\frac{x}{y}-\frac{2}{3}\right)\left(\frac{x}{y}+\frac{2}{3}\right)=\left(\frac{x}{y}\right)^2-\left(\frac{2}{3}\right)^2\)
b,\(\left(2\sqrt{x}-\frac{2}{3}\right)\left(\frac{2}{3}+2\sqrt{x}\right)=\left(2\sqrt{x}-\frac{2}{3}\right)\left(2\sqrt{x}+\frac{2}{3}\right)\)
\(=\left(2\sqrt{x}\right)^2-\left(\frac{2}{3}\right)^2\)
Trả lời:
a, \(\left(\frac{x}{y}-\frac{2}{3}\right)\left(\frac{x}{y}+\frac{2}{3}\right)\)\(=\left(\frac{x}{y}\right)^2-\left(\frac{2}{3}\right)^2=\frac{x^2}{y^2}-\frac{4}{9}\)
b, \(\left(2\sqrt{x}-\frac{2}{3}\right)\left(\frac{2}{3}+2\sqrt{x}\right)=\left(2\sqrt{x}-\frac{2}{3}\right)\left(2\sqrt{x}+\frac{2}{3}\right)=\left(2\sqrt{x}\right)^2-\left(\frac{2}{3}\right)^2=4x-\frac{4}{9}\)
a: \(\left(2x^2+3y\right)^3\)
\(=8x^6+3\cdot4x^4\cdot3y+3\cdot2x^2\cdot9y^2+27y^3\)
\(=8x^6+36x^4y+54x^2y^2+27y^3\)
b: \(\left(2a^2b+\dfrac{1}{3}ab^2\right)^2\)
\(=4a^4b^2+2\cdot2a^2b\cdot\dfrac{1}{3}ab^2+\dfrac{1}{9}a^2b^4\)
\(=4a^4b^2+\dfrac{4}{3}a^3b^3+\dfrac{1}{9}a^2b^4\)
\(27a^3-b^3+9ab^2-27a^2b\)
\(=\left(3a\right)^3-3\cdot\left(3a\right)^2b+3\cdot3a\cdot b^2-b^3\)
\(=\left(3a-b\right)^3\)
a) 16x2 - ( x2 + 4 )2
= ( 4x )2 - ( x2 + 4 )2
= [ 4x - ( x2 + 4 ) ][ 4x + ( x2 + 4 ) ]
= ( -x2 + 4x - 4 )( x2 + 4x + 4 )
= [ -( x2 - 4x + 4 ) ]( x + 2 )2
= [ -( x - 2 )2 ]( x + 2 )2
b) ( x + y )3 + ( x - y )3
= [ ( x + y ) + ( x - y ) ][ ( x + y )2 - ( x + y )( x - y ) + ( x - y )2 ]
= ( x + y + x - y )[ x2 + 2xy + y2 - ( x2 - y2 ) + x2 - 2xy + y2 ]
= 2x( 2x2 + 2y2 - x2 + y2
= 2x( x2 + 3y2 )
a) \(x^2+4x+3=\left(x^2+4x+4\right)-1=\left(x+2\right)^2-1^2=\left(x+1\right)\left(x+3\right)\) (mình sửa lại)
b) \(x^2+8x-9=\left(x^2+8x+16\right)-25=\left(x+4\right)^2-5^2=\left(x-1\right)\left(x+9\right)\)
c) \(3x^2+6x-9=3\left[\left(x^2+2x+1\right)-4\right]=3\left[\left(x+1\right)^2-2^2\right]=3\left(x-1\right)\left(x+3\right)\)
d) \(2x^2+x-3=2x^2-4x+2+5x-5=2\left(x^2-2x+1\right)+5\left(x-1\right)=2\left(x-1\right)^2+5\left(x-1\right)=\left(x-1\right)\left(2x+3\right)\)
( 2x - 3y )2 = 4x2 - 12xy + 9y2
( 3√x - y )2 = 9x - 6y√x + y2 ( x ≥ 0 )