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A = x ( x + y ) - y ( x + y )
A = ( x + y ) ( x - y )
A = x\(^2\) - y\(^2\)
Tại x = \(\dfrac{-1}{2}\) và y = -2 ta có
\(\left(\dfrac{-1}{2}\right)^2-\left(-2\right)^2\) \(=\) \(\dfrac{-15}{4}\)
\(a\\ -5x^2+3x.\left(x+2\right)=-5x^2+3x^2+6x=-2x^2+6x\\ b\\ -2x.\left(1-x^2\right)-2x^3=-2x+2x^3-2x^3=-2x\\ c\\ 4x.\left(x-1\right)-4.\left(x^2+2x-1\right)\\ =4x^2-4x-4x^2-8x+4=-12x+4\)
\(d\\ 6x^3-2x^2.\left(-x^2-3x\right)=6x^3+2x^4+6x^3=2x^4+12x^3\\ e\\ 3x.\left(x-1\right)-\left(1+2x\right).5x\\ =3x^2-3x-5x-10x^2=-7x^2-8x\\ f\\ -5x^2-\left(x-6\right).\left(-2x^2\right)=-5x^2+2x^3-12x^2=2x^3-17x^2\)
\(\left(x-2\right)\left(2x^3-x^2+1\right)+\left(x-2\right).x^2.\left(1-2x\right)\)
\(=\left(x-2\right)\left(2x^3-x^2+1\right)+\left(x-2\right)\left(x^2-2x^3\right)\)
\(=\left(x-2\right)\left(2x^3-x^2+1+x^2-2x^3\right)\)
\(=\left(x-2\right).1\)
\(=x-2\)
Ta có:
\(\left(x-2\right)\left(2x^3-x^2+1\right)+\left(x-2\right)x^2\left(1-2x\right)\)
\(=\left(x-2\right)\left(2x^3-x^2+1\right)+\left(x-2\right)\left(x^2-2x^3\right)\)
\(=\left(x-2\right)\left[\left(2x^3-x^2+1\right)+\left(x^2-2x^3\right)\right]\)
\(=\left(x-2\right)\left(2x^3-x^2+1+x^2-2x^3\right)\)
\(=\left(x-2\right).1\)
\(=x-2\)
Lời giải:
$H=(x^3-3x^2+3x-1)-(x^3+8)+3(x^2-16)$
$=x^3-3x^2+3x-1-x^3-8+3x^2-48$
$=(x^3-x^3)+(-3x^2+3x^2)+3x+(-1-8-48)$
$=3x-57=3.\frac{-1}{2}-57=\frac{-117}{2}$
(2x - 1)2 + 2(2x - 1)(x + 1) + (x - 1)2 (Dễ dàng nhận thấy đây là HĐT số 1)
= (2x -1 + x - 1)2
= (3x - 2)2
a) \(|x|-x\)
\(\Rightarrow\orbr{\begin{cases}x< 0\rightarrow\left|x\right|-x=2\left|x\right|\\x>0\rightarrow\left|x\right|-x=0\end{cases}}\)
\(\Rightarrow x=0\rightarrow x=0\)
(x – 2) . (2x3 – x2 + 1) + (x – 2) x2(1 – 2x)
= (x – 2). [(2x3 – x2 + 1) + x2(1 – 2x)]
= (x – 2). [2x3 – x2 + 1 + x2 . 1 + x2 . (-2x)]
= (x – 2) . (2x3 – x2 + 1 + x2 – 2x3)
= (x – 2) .1
= x – 2
A = (x - 2)2 + (x + 3)2 - 2.(x + 1)(x - 1)
A = (x - 2)2 + (x + 3)2 - 2.(x2 - 1)
A = x2 - 2.2x + 22 + x2 + 2.3x + 32 - 2x2 + 2
A = 2x + 15
\(A=\left(x-2\right)^2+\left(x+3\right)^2-2\left(x+1\right)\left(x-1\right)\)
\(A=x^2-4x+4+x^2+6x+9-2\left(x^2-1\right)\)
\(A=2x^2+2x+13-2x^2+2\)
\(A=2x+15\)