Rút gọn:
A= \(\left(x-3\right)^3-\left(x+3\right)^3\)
B=\(\left(x+2\right)^3-\left(x-2\right)^3-12x^2\)
Rút gọn biểu thức:
\(a)A=\left(x-2\right)\left(x+2\right)\left(x+3\right)-\left(x-1\right)^3\\ b)\left(x+2\right)^3-\left(x-2\right)^3-12x^2\)
rút gọn các phân thức:
a,\(\frac{a^2\left(b-c\right)+b^2\left(c-a\right)+c^2\left(a-b\right)}{ab^2-ac^2-b^3+bc^2}\)b,\(\frac{2x^3-7x^2-12x+45}{3x^3-19x^2+33x-9}\)c,\(\frac{x^3-y^3+z^3+3xyz}{\left(x+y\right)^2+\left(y+z\right)^2+\left(z-x\right)^2}\)
AD phân tích đa thức thành nhân tử ở tử thức và mẫu thức của từng phân thức
Rút gọn
a) \(\left(x+2y\right)^2+4y\)
b) \(\left(2x-3\right)\left(2x+3\right)-4x^2\)
c)\(\left(3x+1\right)^2-\left(x+1\right)\left(x-1\right)\)
Lời giải:
a. Biểu thức này không có khả năng rút gọn. Khai triển ra cũng được nhưng không làm gọn được bạn nhé.
b. $=(2x)^2-3^2-4x^2=4x^2-9-4x^2=-9$
c. $=(3x)^2+2.3x+1^2-(x^2-1)=9x^2+6x+1-x^2+1=8x^2+6x+2$
Rút gọn biểu thức
a) \(2\left(x+y\right)^3+2\left(x-y\right)^3\)
b) \(\left(x-y\right)^3-\left(x+y\right)^3-3\left(x+y\right)^2\left(x-y\right)-3\left(x+y\right)\left(x-y\right)^2\)
Bài làm
a) 2(x + y)3 + 2(x - y)3
= 2[(x + y)3 + (x - y)3]
= 2[x3 + 3x2y + 3xy2 + y3 + x3 - 3x2y + 3xy2 - y3]
= 2[(x3 + x3) + (3x2y - 3x2y) + (3xy2 + 3xy2) + (y3 - y3)]
= 2[2x3 + 6xy2]
= 4x3 + 12xy2
b)uhm... Mình sửa đề chút, thay vì là -3(x + y)2(x - y) thì mình sẽ thành +3(x + y)2(x - y)
(x - y)3 - (x + y)3 + 3(x + y)2(x - y) - 3(x + y)(x - y)2
= -[(x + y)3 - 3(x + y)2(x - y) + 3(x + y)(x - y)2 - (x - y)3]
= -[(x + y) - (x - y)]3
= -[x + y - x + y ]3
= -[y]3
= -y
Rút gọn biểu thức A = \(\sqrt{\dfrac{\left(x^2-3\right)^2+12x^2}{x^2}}+\sqrt{\left(x+2\right)^2-8x}\)
đk: x khác 0
A = \(\sqrt{\dfrac{x^4-6x^2+9+12x^2}{x^2}}+\sqrt{x^2+4x+4-8x}\)
= \(\sqrt{\dfrac{x^4+6x^2+9}{x^2}}+\sqrt{x^2-4x+4}\)
= \(\sqrt{\dfrac{\left(x^2+3\right)^2}{x^2}}+\sqrt{\left(x-2\right)^2}\)
= \(\dfrac{x^2+3}{\left|x\right|}+\left|x-2\right|\)
TH1: x \(\ge2\)
A = \(\dfrac{x^2+3}{x}+x-2\)
= \(\dfrac{x^2+3+x^2-2x}{x}=\dfrac{2x^2-2x+3}{x}\)
TH2: \(0< x< 2\)
A = \(\dfrac{x^2+3}{x}-x+2\)
= \(\dfrac{x^2+3-x^2+2x}{x}=\dfrac{2x+3}{x}\)
TH3: x < 0
A = \(\dfrac{x^2+3}{-x}-x+2\)
= \(\dfrac{-x^2-3}{x}-x+2=\dfrac{-x^2-3-x^2+2x}{x}=\dfrac{-2x^2+2x-3}{x}\)
\(\sqrt{\dfrac{\left(x^2-3\right)^2+12x^2}{x^2}+\sqrt{\left(x+2\right)^2-8x}}\) Rút gọn
rút gọn:
\(A=3\left(x-1\right)^2-\left(x+1\right)^2+2\left(x-3\right)\left(x+3\right)-\left(2x+3\right)^2-\left(5-20x\right)\)
Theo ý kiến của mình thì:
\(A=3\left(x-1\right)^2-\left(x+1\right)^2+2\left(x-3\right)\left(x+3\right)-\left(2x+3\right)^2-\left(5-20\right)\)
\(A=3\left(x-1-x-1\right)\left(x-1+x+1\right)+2\left(x-3\right)^2-\left(2x+3\right)^2+15\)
\(A=3\left(-2\right)\left(2x\right)+2\left(x-3-2x-3\right)\left(x-3+2x+3\right)+15\)
\(A=-12x+2\left(-6-x\right)\left(3x\right)+15\)
\(A=-12x-36x-6x^2+15\)
\(A=-6x\left(2+6+x\right)+15\)
\(A=-6x\left(8+x\right)+15\)
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
a. Q= \(\left(x-y\right)^2\)-4(x-y)(x+2y)+4\(\left(x+2y\right)^2\)
b. A=\(\left(xy+2\right)^3\)-6\(\left(xy+2\right)^2\)+12(xy+2)-8
c. \(\left(x+2\right)^3\)+\(\left(x-2\right)^3\)-2x(\(x^2\)+12)
a) \(Q=\left(x-y\right)^2-4\left(x-y\right)\left(x+2y\right)+4\left(x+2y\right)^2\)
\(Q=\left(x-y\right)^2-2\cdot\left(x-y\right)\cdot2\left(x+2y\right)+\left[2\left(x+2y\right)\right]^2\)
\(Q=\left[\left(x-y\right)-2\left(x+2y\right)\right]^2\)
\(Q=\left(x-y-2x-4y\right)^2\)
\(Q=\left(-x-5y\right)^2\)
b) \(A=\left(xy+2\right)^3-6\left(xy+2\right)^2+12\left(xy+2\right)-8\)
\(A=\left(xy+2\right)^3-3\cdot2\cdot\left(xy+2\right)^2+3\cdot2^2\cdot\left(xy+2\right)-2^3\)
\(A=\left[\left(xy+2\right)-2\right]^3\)
\(A=\left(xy+2-2\right)^3\)
\(A=\left(xy\right)^3\)
\(A=x^3y^3\)
c) \(\left(x+2\right)^3+\left(x-2\right)^3-2x\left(x^2+12\right)\)
\(=\left(x^3+6x^2+12x+8\right)+\left(x^2-6x^2+12x-8\right)-\left(2x^3+24x\right)\)
\(=x^3+6x^2+12x+8+x^2-6x^2+12x-8-2x^3-24x\)
\(=\left(x^3+x^3-2x^3\right)+\left(6x^2-6x^2\right)+\left(12x+12x-24x\right)+\left(8-8\right)\)
\(=0\)
a: =(x-y)^2-2(x-y)(2x+4y)+(2x+4y)^2
=(x-y-2x-4y)^2=(-x-5y)^2=x^2+10xy+25y^2
b: =(xy+2-2)^3=(xy)^3=x^3y^3
c: =x^3+6x^2+12x+8+x^3-6x^2+12x-8-2x(x^2+12)
=24x+2x^3-2x^3-24x
=0