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d. 2x2(x - y) + 2y(y - x)
= 2x2(x - y) - 2y(x - y)
= (2x2 - 2y)(x - y)
= 2(x2 - y)(x - y)
e. 5a2b(a - 2b) - 2a(2b - a)
= 5a2b(a - 2b) + 2a(a - 2b)
= (5a2b + 2a)(a - 2b)
= a(5ab + 2)(a - 2b)
f. 4x2y(x - y) + 9xy2(x - y)
= (4x2y + 9xy2)(x - y)
= xy(4x + 9y)(x - y)
g. 50x2(x - y)2 - 8y2(y - x)2
= 50x2(x2 - 2xy + y2) - 8y2(y2 - 2xy + x2)
= 50x2(x2 - 2xy + y2) - 8y2(x2 - 2xy + y2)
= 50x2(x - y)2 - 8y2(x - y)2
= (50x2 - 8y2)(x - y)2
= 2(25x2 - 4y2)(x - y)2.
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a) C có nghĩa ⇔\(\left\{{}\begin{matrix}2x-2\ne0\\2x^2-2\ne0\end{matrix}\right.\)
⇔ \(\left\{{}\begin{matrix}x\ne1\\x\ne-1\end{matrix}\right.\)
b)C= \(\dfrac{x}{2x-2}-\dfrac{x^2+1}{2x^2-2}\)
= \(\dfrac{x\left(x+1\right)}{2\left(x-1\right)\left(x+1\right)}\)-\(\dfrac{x^2+1}{2\left(x+1\right)\left(x-1\right)}\)
= \(\dfrac{x^2+x}{2\left(x-1\right)\left(x+1\right)}-\dfrac{x^2+1}{2\left(x-1\right)\left(x+1\right)}\)
= \(\dfrac{1}{2\left(x+1\right)}\)
c) Ta có x2-x=0 ⇒ \(\left\{{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
Thay x=0 vào C= \(\dfrac{1}{2\left(x+1\right)}\) ⇒ C= \(\dfrac{1}{2}\)
Thay x= 1 vào C = \(\dfrac{1}{2\left(x+1\right)}\) ⇒ C= \(\dfrac{1}{4}\)
d) C= \(\dfrac{1}{2\left(x+1\right)}\)= \(\dfrac{-1}{2}\)
⇔-2(x+1)=2 ⇔ x=-2
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a) \(A=\dfrac{1}{x+5}+\dfrac{2}{x-5}-\dfrac{2x+10}{\left(x+5\right)\left(x-5\right)}\)
\(A=\dfrac{x-5+2x+10-2x-10}{\left(x+5\right)\left(x-5\right)}=\dfrac{x-5}{\left(x+5\right)\left(x-5\right)}=\dfrac{1}{x+5}\)
b) \(A=-3\Rightarrow\dfrac{1}{x+5}=-3\)
\(\Leftrightarrow x+5=-\dfrac{1}{3}\Leftrightarrow x=-\dfrac{1}{3}-5=\dfrac{-16}{3}\)
\(9x^2-42x+49=\left(3x-7\right)^2=\left(3.\dfrac{-16}{3}-7\right)^2=\left(-23\right)^2=529\) \(\left(x=\dfrac{-16}{3}\right)\)
A = ( 5a + 1/2 )2 - 2( 25a2 - 1/4 ) + ( 5a - 1/2 )2
= ( 5a + 1/2 )2 - 2[ ( 5a )2 - ( 1/2 )2 ] + ( 5a - 1/2 )2
= ( 5a + 1/2 )2 - 2( 5a - 1/2 )( 5a + 1/2 ) + ( 5a - 1/2 )2
= [ ( 5a + 1/2 ) - ( 5a - 1/2 ) ]
= ( 5a + 1/2 - 5a + 1/2 )2
= 12 = 1