Giúp mik vs
1. Rút gọn các biểu thức
a/ ( x + 1 )2 - ( x - 1 )2 - 3 ( x + 1 ) . ( x - 1)
b/ 5 ( x + 2 ) ( x - 2) - 1/2 ( 6- 8x)4 + 17
thanks
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
ND
1
6 tháng 7 2021
a) Ta có: \(\left(x+1\right)^2-\left(x-1\right)^2-3\left(x+1\right)\left(x-1\right)\)
\(=x^2+2x+1-x^2+2x-1-3\left(x^2-1\right)\)
\(=4x-3x^2+3\)
\(=-3x^2+4x+3\)
b) Ta có: \(5\left(x+2\right)\left(x-2\right)-\dfrac{1}{2}\left(6-8x\right)^2+17\)
\(=5\left(x^2-4\right)-\dfrac{1}{2}\left(64x^2-96x+36\right)+17\)
\(=5x^2-20-32x^2+48x-16+17\)
\(=-27x^2+48x-19\)
22 tháng 10 2023
1:
a: \(\left(2x-5\right)^2-4x\left(x+3\right)\)
\(=4x^2-20x+25-4x^2-12x\)
=-32x+25
b: \(\left(x-2\right)^3-6\left(x+4\right)\left(x-4\right)-\left(x-2\right)\left(x^2+2x+4\right)\)
\(=x^3-6x^2+12x-8-\left(x^3-8\right)-6\left(x^2-16\right)\)
\(=-6x^2+12x-6x^2+96=-12x^2+12x+96\)
c: \(\left(x-1\right)^2-2\left(x-1\right)\left(x+2\right)+\left(x+2\right)^2+5\left(2x-3\right)\)
\(=\left(x-1-x-2\right)^2+5\left(2x-3\right)\)
\(=\left(-3\right)^2+5\left(2x-3\right)\)
\(=9+10x-15=10x-6\)
2:
a: \(\left(2-3x\right)^2-5x\left(x-4\right)+4\left(x-1\right)\)
\(=9x^2-12x+4-5x^2+20x+4x-4\)
\(=4x^2+12x\)
b: \(\left(3-x\right)\left(x^2+3x+9\right)+\left(x-3\right)^3\)
\(=27-x^3+x^3-9x^2+27x-27\)
\(=-9x^2+27x\)
c: \(\left(x-4\right)^2\left(x+4\right)-\left(x-4\right)\left(x+4\right)^2+3\left(x^2-16\right)\)
\(=\left(x-4\right)\left(x+4\right)\left(x-4-x-4\right)+3\left(x^2-16\right)\)
\(=\left(x^2-16\right)\left(-8\right)+3\left(x^2-16\right)\)
\(=-5\left(x^2-16\right)=-5x^2+80\)
22 tháng 11 2021
\(a,\Leftrightarrow\left[{}\begin{matrix}3x+2=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{2}{3}\left(l\right)\\x=-2\left(l\right)\end{matrix}\right.\Leftrightarrow x\in\varnothing\Leftrightarrow A\in\varnothing\\ b,\text{ý bạn là rút gọn A hả?}\\ A=\dfrac{x-2+2x+3x+6}{\left(x-2\right)\left(x+2\right)}=\dfrac{6x+4}{\left(x-2\right)\left(x+2\right)}\)
3 tháng 8 2023
\(A=\dfrac{2\sqrt{x}-9-\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right)-\left(2\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}\)
\(=\dfrac{2\sqrt{x}-9-x+2\sqrt{x}+3-2x+3\sqrt{x}+2}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}\)
\(=\dfrac{-3x+7\sqrt{x}-4}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}\)
H9
HT.Phong (9A5)
CTVHS
3 tháng 8 2023
\(A=\dfrac{2\sqrt{x}-9}{x-5\sqrt{x}+6}-\dfrac{\sqrt{x}+1}{\sqrt{x}-2}+\dfrac{2\sqrt{x}+1}{3-\sqrt{x}}\) (ĐK: \(x\ne4;x\ne9;x\ge0\))
\(A=\dfrac{2\sqrt{x}-9}{x-2\sqrt{x}-3\sqrt{x}+6}-\dfrac{\sqrt{x}+1}{\sqrt{x}-2}+\dfrac{2\sqrt{x}+1}{3-\sqrt{x}}\)
\(A=\dfrac{2\sqrt{x}-9}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}-\dfrac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}-\dfrac{\left(2\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}-2\right)}\)
\(A=\dfrac{2\sqrt{x}-9-\left(\sqrt{x}+1\right)\left(\sqrt{x}-3\right)-\left(2\sqrt{x}+1\right)\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)
\(A=\dfrac{2\sqrt{x}-9-\left(x-3\sqrt{x}+\sqrt{x}-3\right)-\left(2x-4\sqrt{x}+\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)
\(A=\dfrac{2\sqrt{x}-9-x+2\sqrt{x}+3-2x+3\sqrt{x}+2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)
\(A=\dfrac{-3x+7\sqrt{x}-4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-3\right)}\)
SS
1
Y
26 tháng 5 2023
\(a,3x\left(x-2\right)-5x\left(1-x\right)-8\left(x^2-3\right)\)
\(=3x^2-6x-5x+5x^2-8x^2+24\)
\(=\left(3x^2+5x^2-8x^2\right)+\left(-6x-5x\right)+24\)
\(=0-11x+24\)
\(=-11x+24\)
\(b,\left(7x-3\right)\left(2x+1\right)-\left(5x-2\right)\left(x+4\right)-9x^2+17x\)
\(=14x^2+7x-6x-3-5x^2-20x+2x+8-9x^2+17x\)
\(=\left(14x^2-5x^2-9x^2\right)+\left(7x-6x-20x+2x+17x\right)+\left(-3+8\right)\)
\(=0+0+5\)
\(=5\)
24 tháng 6 2023
a: \(=\dfrac{\left(x+1\right)\left[\left(3x-2\right)-\left(2x+5\right)\left(x-1\right)\right]}{x+1}\)
=3x-2-2x^2+2x-5x+5
=-2x^2+3
b: \(=\left(2x+1-3+x\right)^2=\left(3x-2\right)^2=9x^2-12x+4\)
c: =x^3-3x^2+3x-1-x^3-1+9x^2-1
=6x^2+3x-3
Y
24 tháng 6 2023
\(a,\left[\left(3x-2\right)\left(x+1\right)-\left(2x+5\right)\left(x^2-1\right)\right]:\left(x+1\right)\)
\(=\left[\left(3x-2\right)\left(x+1\right)-\left(2x+5\right)\left(x-1\right)\left(x+1\right)\right]:\left(x+1\right)\)
\(=\left[\left(x+1\right)\left(3x-2-\left(2x+5\left(x-1\right)\right)\right)\right]:\left(x+1\right)\)
\(=\left[\left(x+1\right)\left(3x-2-2x^2+2x-5x+5\right)\right]:\left(x+1\right)\)
\(=\left[\left(x+1\right)\left(-2x^2+3\right)\right].\dfrac{1}{x+1}\)
\(=-2x^2+3\)
\(b,\left(2x+1\right)^2-2\left(2x+1\right)\left(3-x\right)\)
\(=\left(2x+1\right)\left[\left(2x+1\right)-2\left(3-x\right)\right]\)
\(=\left(2x+1\right)\left(2x+1-6+2x\right)\)
\(=\left(2x+1\right)\left(4x-5\right)\)
\(c,\left(x-1\right)^3-\left(x+1\right)\left(x^2-x+1\right)-\left(3x+1\right)\left(1-3x\right)\)
\(=x^3-3x^2+3x-1-x^3-1-\left(3x-9x^2+1-3x\right)\)
\(=-3x^2+3x-2-3x+9x^2-1+3x\)
\(=6x^2+3x-3\)
TM
2 tháng 9 2021
a/ \(A=\left(x-1\right)^3-4x\left(x+1\right)\left(x-1\right)+3\left(x-1\right)\left(x^2+x+1\right)\)
\(=x^3-3x^2+3x-1-4x^3+4x+3x^3-3\)
\(=-3x^2+7x-4\)
Thay x = 2 vào A được:
\(=-3.2^2+7.2-4=-2\)
Vậy: Giá trị của A khi x = 2 là -2
==========
b/ \(B=126y^3+\left(x-5y\right)\left(x^2+25y^2+5xy\right)\)
\(=126y^3+x^3-125y^3\)
Thay x = -5 và y = -3 vào B được:
\(126.\left(-3\right)^3+\left(-5\right)^3-125.\left(-3\right)^3=-152\)
Vậy: Giá trị của B tại x = -5 và y = -3 là -152
==========
c/ \(C=a^3+b^3-\left(a^2-2ab+b^2\right)\left(a-b\right)\)
\(=a^3+b^3-\left(a-b\right)^3\)
\(=a^3+b^3-a^3+3a^2b-3ab^2+b^3\)
\(=2b^3+3a^2b-3ab^2\)
Thay a = -4 và b = 4 vào C được:
\(2.4^3+3.\left(-4\right)^2.4-3.\left(-4\right).4^2=512\)
Vậy: Giá trị của C tại a = -4 vào b = 4 là 512
2 tháng 9 2021
a:Ta có: \(A=\left(x-1\right)^3-4x\left(x+1\right)\left(x-1\right)+3\left(x-1\right)\left(x^2+x+1\right)\)
\(=x^3-3x^2+3x-1-4x^3+4x+3x^3-3\)
\(=-3x^2+7x-4\)
\(=-3\cdot2^2+7\cdot2-4\)
\(=-12-4+14=-2\)
c: Ta có: \(C=a^3+b^3-\left(a-b\right)\left(a^2-2ab+b^2\right)\)
\(=a^3+b^3-a^3+3a^2b-3ab^2+b^3\)
\(=2b^3+3a^2b-3ab^2\)
\(=2\cdot4^3+3\cdot\left(-4\right)^2\cdot4-3\cdot\left(-4\right)\cdot4^2\)
\(=128+192+192=512\)
Mình làm thử nha:
a/ \(\left(x+1\right)^2-\left(x-1\right)^2-3\left(x+1\right).\left(x-1\right)\)
\(=\left(x+1\right)\left(x+1\right)-\left(x-1\right)\left(x-1\right)-\left(3x+3\right).\left(x-1\right)\)
\(=\left[\left(x+1\right)\left(x+1\right)-\left(x-1\right)\left(x-1\right)\right]-4x+\left(-3\right)\)
Từ đó làm tiếp
b/ \(5\left(x+2\right)\left(x-2\right)-\frac{1}{2}\left(6-8x\right)^4+17\)
\(=\left(5x+10\right)\left(x-2\right)-\left(3-4x\right)^4+17\)
\(=6x+\left(-20\right)-\left(81-256x\right)+17\)
Làm nốt nha