rút gọn biểu thức: \(3\left(x-1\right)-2\left|x-3\right|\)
\(\left(x^2_{ }+1\right)\left(x-3\right)-\left(x-3\right)\left(x^2-1\right)\)
rút gọn biểu thức
\(=\left(x-3\right)\left(x^2+1-x^2+1\right)=2\left(x-3\right)\)
(x2 + 1)(x - 3) - (x - 3)(x2 - 1)
= [x2 + 1 - (x2 - 1)](x - 3)
= (x2 + 1 - x2 + 1)(x - 3)
= 2(x - 3)
`=(x-3)[x^2+1-(x^2-1)]`
`=(x-3)(x^2+1-x^2+1)`
`=2(x-3)`
Rút gọn các biểu thức sau
a, \(2x\left(2x-1\right)^2-3x\left(x+3\right)\left(x-3\right)-4x\left(x+1\right)^2\)
a: \(2x\left(2x-1\right)^2-3x\left(x+3\right)\left(x-3\right)-4x\left(x+1\right)^2\)
\(=2x\left(4x^2-4x+1\right)-3x\left(x^2-9\right)-4x\left(x^2+2x+1\right)\)
\(=8x^3-8x^2+2x-3x^3+27x-4x^3-8x^2-4x\)
\(=x^3-16x^2+25x\)
rút gọn biểu thức \(\left(x-3\right)\left(x^2+3x+9\right)-\left(2x-1\right)^2\)
\(=x^3-27-4x^2+4x-1=x^3-4x^2+4x-28\)
Rút gọn biểu thức:
\(\left(x-1\right)^2-2\left(x-2\right)\left(x+2\right)-3\left(x+2\right)^3\)
\(=\left(x-1\right)^2-\left(x+2\right)\left[2\left(x-2\right)+3\left(x+2\right)^2\right]\)
\(=x^2-2x+1-\left(x+2\right)\left[2x-4+3\left(x^2+4x+4\right)\right]\)
\(=x^2-2x+1-\left(x+2\right)\left(3x^2+14x+8\right)\)
\(=x^2-2x+1-\left(3x^3+6x^2+14x^2+28x+8x+16\right)\)
\(=-3x^3-21x^2-38x-15\)
Rút gọn biểu thức : \(2\left|x-3\right|-\left|4x-1\right|\)
Rút gọn các biểu thức sau:
a/ \(\left(x-2y^{ }\right)^2+\left(x-\dfrac{1}{2}y\right)\left(x+\dfrac{1}{2}y\right)\)
b/ \(\left(x-2\right)^2+\left(x+3\right)^2-2\left(x-1\right)\left(x+1\right)\)
a: \(\left(x-2y\right)^2+\left(x-\dfrac{1}{2}y\right)\left(x+\dfrac{1}{2}y\right)\)
\(=x^2-4xy+4y^2+x^2-\dfrac{1}{4}y^2\)
\(=2x^2-4xy+\dfrac{15}{4}y^2\)
b: \(\left(x-2\right)^2+\left(x+3\right)^2-2\left(x-1\right)\left(x+1\right)\)
\(=x^2-4x+4+x^2+6x+9-2\left(x^2-1\right)\)
\(=2x^2+2x+13-2x^2+2\)
=2x+15
a) \(=x^2-4xy+4y^2+x^2-\dfrac{1}{4}y^2=2x^2-4xy+\dfrac{15}{4}y^2\)
b) \(=x^2-4x+4+x^2+6x+9-2x^2+2\)
\(=2x+15\)
a; \(\left(x-2y\right)^2+\left(x-\dfrac{1}{2}y\right)\left(x+\dfrac{1}{2}y\right)\)
= \(x^2-4xy+4y^2+x^2-\dfrac{1}{4}y^2\)
= \(2x^2-4xy+\dfrac{15}{4}y^2\)
b; \(\left(x-2\right)^2+\left(x+3\right)^2-2\left(x-1\right)\left(x+1\right)\)
= \(x^2-4x+4+x^2+6x+9-2x^2+2\)
= \(2x+15\)
RÚT GỌN BIỂU THỨC SAU
\(\left(x-2\right)^3-x\left(x+1\right)\left(x-1\right)+6x\left(x-3\right)\)
MẤY BẠN GIÚP MK VS Ạ AI NHANH MK VOTE NHA
\(=x^6-6x^4+12x^2-8-x^3+x+6x^2-18x\\ =x^6-6x^4-x^3+18x^2-17x-8\)
Rút gọn các biểu thức sau:
A= \(3\left(x+2\sqrt{x}\right)-\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\)
B= \(\left(\sqrt{x}+1\right)\left(\sqrt{x}+3\right)-2\left(\sqrt{x}-1\right)^2\)
C= \(3x-3\sqrt{x}-2+\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\)
D= \(\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)-\left(2\sqrt{x}+1\right)\left(\sqrt{x}-2\right)\)
E= \(\left(\sqrt{x}+4\right)\left(\sqrt{x}-4\right)-\left(2\sqrt{x}-1\right)\left(\sqrt{x}+2\right)\)
\(A=3\left(x+2\sqrt{x}\right)-\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\)
\(=3x+6\sqrt{x}-\left(x-1\right)\)
\(=3x+6\sqrt{x}-x+1\)
\(=2x+6\sqrt{x}+1\)
\(B=\left(\sqrt{x}+1\right)\left(\sqrt{x}+3\right)-2\left(\sqrt{x}-1\right)^2\)
\(=x+3\sqrt{x}+\sqrt{x}+3-2\left(x-2\sqrt{x}+1\right)\)
\(=x+4\sqrt{x}+3-2x+4\sqrt{x}-2\)
\(=-x+8\sqrt{x}+1\)
\(C=3x-3\sqrt{x}-2+\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)\)
\(=3x-3\sqrt{x}-2+\left(\sqrt{x^2}-1\right)\)
\(=3x-3\sqrt{x}-2+x-1\)
\(=4x-3\sqrt{x}-3\)
\(D=\left(\sqrt{x}+3\right)\left(\sqrt{x}-3\right)-\left(2\sqrt{x}+1\right)\left(\sqrt{x}-2\right)\)
\(=x-9-\left(2x-3\sqrt{x}-2\right)\)
\(=x-9-2x+3\sqrt{x}+2\)
\(=-x+3\sqrt{x}-7\)
\(E=\left(\sqrt{x}+4\right)\left(\sqrt{x}-4\right)-2\left(2\sqrt{x}-1\right)\left(\sqrt{x}+2\right)\)
\(=\sqrt{x^2}-2^2-2\left(2x+4\sqrt{x}-\sqrt{x}-2\right)\)
\(=x-4-2\left(2x+3\sqrt{x}-2\right)\)
\(=x-4-4x-6\sqrt{x}+4\)
\(=-3-6\sqrt{x}\)
Rút gọn biểu thức bằng cách nhanh nhất
\(\left(x-1\right)^3+4\left(x+1\right)\left(1-x\right)+3\left(x-1\right)\left(x^2+x+1\right)\)
\(\left(x-1\right)^3+4\left(x+1\right)\left(1-x\right)+3\left(x-1\right)\left(x^2+x+1\right).\)
\(=\left(x-1\right)^3+4\left(x+1\right)\left(1-x\right)+3\left(x-1\right)^3.\)
\(=\left(x-1\right)^3+4\left(1-x^2\right)+3\left(x-1\right)^3.\)
\(=\left(x-1\right)^3+3\left(x-1\right)^3+4\left(1-x^2\right)\)
\(=4\left(x-1\right)^3+4\left(1-x^2\right)\)
\(=4\left[\left(x-1\right)^3+\left(1-x^2\right)\right]\)
rút gọn biểu thức \(\left(5-3x\right)^2+\left(x+2\right)^2+x\left(3-4x\right)\)
\(\left(3x-5\right)^2+\left(x+2\right)^2+x\left(3-4x\right)\)
\(=9x^2-30x+25+x^2+4x+4+3x-4x^2\)
\(=6x^2-23x+29\)
\(=25-30x+9x^2+x^2+4x+4+3x-12x^2=-2x^2-23x+29\)