Rút gọn biểu thức:
a) \(A=\left(x-y\right)^3+\left(y+x\right)^3+\left(y-x\right)^3-3xy\left(x+y\right)\)
b) \(B=3x^2\left(x+1\right)\left(x-1\right)-\left(x^2-1\right)\left(x^4+x^2+1\right)+\left(x^2-1\right)^3\)
c) \(C=\left(x+y\right)\left(x^2-xy+y^2\right)+\left(x-y\right)\left(x^2+xy+y^2\right)-2x^3\)
d) \(D=\left(x+1\right)^3+\left(x-1\right)^3+x^3-3x\left(x+1\right)\left(x-1\right)\)
Nhìn tổng quan để nhận ra kiến thức rồi thu gọn
\(A=\left(x-1\right)^2-\left(2x-2\right)\left(2x+3\right)+\left(2x+3\right)^2-x\left(x+8\right)\)
\(B=\left(x+y-1\right)\left(x-y+1\right)+\left(y-1\right)^2\)
Bài 1: Cm giá trị của biểu thức sau không phụ thuộc vào biến x:
a) \(\left(2x+3\right).\left(4x^2-6x+9\right)-2\left(4x^3-1\right)\)
b)\(\left(x+3\right)^3+\left(x+9\right).\left(x^2+27\right)\)
c)\(\left(x+y\right).\left(x^2-xy+y^2\right)+\left(x-y\right).\left(x^2+xy+y^2\right)-2x^3\)
Bài 2: Tìm x biết:
a) \(\left(x+2\right)^2-9=0\)
b) \(\left(x+2\right)^2-x^2+4=0\)
c) \(\left(x-3\right)^2-4=0\)
d) \(x^2-2x=24\)
e) \(\left(2x-1\right)^2+\left(x+3\right)^2-5\left(x-7\right)\left(x+7\right)=0\)
Tính
\(1.\left(x+2y\right)^2\)
\(2.\left(2x+3y\right)^2\)
\(3.\left(x+\frac{1}{3}\right)^4\)
\(4.\left(2x+y^2\right)^3\)
\(5.\left(\frac{x}{2}-2y\right)\)
\(6.\left(\sqrt{2x-y}\right)^4\)
\(7.\left(x+1\right)\left(x^2-x+1\right)\)
\(8.\left(x-3\right)\left(x^2+3x+9\right)\)
Rút gọn biểu thức :
a) \(2\left(x-y\right)\left(x+y\right)+\left(x+y\right)^2+\left(x-y\right)^2\)
b) P=\(\left(5x-1\right)+2\left(1-5x\right)\left(4+5x\right)+\left(5x+4\right)^2\)
c) Q=\(\left(x-y\right)^3+\left(y+x\right)^3+\left(y-x\right)^3-3xy\left(x+y\right)\)
d) P = \(12\left(5^2+1\right)\left(5^4+1\right)\left(5^8+1\right)\left(5^{16}+1\right)\)
1. tính
a) \(\left(\dfrac{2}{3}x-\dfrac{3}{2}y\right)^2\)
b) \(\left(\dfrac{1}{2}x^2+\dfrac{1}{3}\right)^2\)
c) \(\left(x+\dfrac{1}{5}y^2\right)\left(x-\dfrac{1}{5}y^2\right)\)
d) \(\left(\dfrac{1}{2}x-2y\right)^3\)
e) \(\left(-\dfrac{1}{2}xy^2+x\right)^3\)
f) \(27x^3-8y^3\)
g) 4(2x - 3y) - 4 - (2x-3y)2
2. rút gọn
a) \(2m\left(5m+2\right)+\left(2m-3\right)\left(3m-1\right)\)
b) \(\left(2x+4\right)\left(8x-3\right)-\left(4x+1\right)^2\)
c) \(\left(7y-2\right)^2-\left(7y+1\right)\left(7y-1\right)\)
d) \(\left(a+2\right)^3-a\left(a-3\right)^2\)
3. c/m các biểu thức sau ko phụ thuộc vào biến x,y
a) \(\left(2x-5\right)\left(2x+5\right)-\left(2x-3\right)^2-12x\)
b) \(\left(2y-1\right)^3-2y\left(2y-3\right)^2-6y\left(2y-2\right)\)
c) \(\left(x+3\right)\left(x^2-3x+9\right)-\left(20+x^3\right)\)
d) \(3y\left(-3y-2\right)^2-\left(3y-1\right)\left(9y^2+3y+1\right)-\left(-6y-1\right)^2\)
4. Tìm x
a) \(\left(2x+5\right)\left(2x-7\right)-\left(-4x-3\right)^2=16\)
b) \(\left(8x^2+3\right)\left(8x^2-3\right)-\left(8x^2-1\right)^2=22\)
c) \(49x^2+14x+1=0\)
d) \(\left(x-1\right)^3-x\left(x-2\right)^2-\left(x-2\right)=0\)
5. c/m biểu thức luôn dương:
a) \(A=16x^2+8x+3\)
b) \(B=y^2-5y+8\)
c) C= \(2x^2-2x+2\)
d) \(D=9x^2-6x+25y^2+10y+4\)
6. Tìm GTLN và GTNN của các biểu thức sau
a) \(M=x^2+6x-1\)
b) \(N=10y-5y^2-3\)
7. thu gọn
a) \(\left(2+1\right)\left(2^2+1\right)\left(2^3+1\right)...\left(2^{32}+1\right)-2^{64}\)
b) \(\left(5+3\right)\left(5^2+3^2\right)\left(5^4+3^4\right)...\left(5^{\text{64}}+3^{64}\right)+\dfrac{5^{128}-3^{128}}{2}\)
ai giúp em vs huhu
bai 1 : chứng minh
\(a,\left(a-b\right)^3=-\left(b-a\right)^3\)
\(b,\left(a-b\right)^2=\left(a+b^{ }2\right)\)
c, \(\left(x+y\right)^3=x\left(x-3y^{ }\right)^2+y\left(y-3x\right)^2\)
d\(\left(x+y^{ }\right)^3-\left(x-y^{ }\right)^3=2y\left(y^2+3x^2\right)\)
Rút gọn rồi tính giá trị biểu thức :
a) \(A=\left(x+3\right)^2+\left(x-3\right).\left(x+3\right)-2.\left(x+2\right).\left(x-4\right)\); với x = \(-\frac{1}{2}\)
b) \(B=\left(3x+4\right)^2-\left(x-4\right).\left(x+4\right)-10x\); với x = \(-\frac{1}{10}\)
c) \(C=\left(x+1\right)^2-\left(2x-1\right)^2+3.\left(x-2\right).\left(x+2\right)\); với x = 1
d) \(D=\left(x-3\right).\left(x+3\right)+\left(x-2\right)^2-2x.\left(x-4\right)\); với x = -1
Tính:
1) \(\left(5x^2-2\right)\)\(\left(5x^2+2\right)\)
2) \(\left(2a+\frac{1}{2}\right)+\left(2a-\frac{1}{2}\right)\)
3) \(\left(3x^2-y\right)\left(3x^2+y\right)\)
4) \(\left(\frac{1}{2}x-1\right)\left(\frac{1}{2}x+1\right)\)
5) \(\left(\frac{3}{4}x+2\right)\left(\frac{3}{4}x-2\right)\)
6) \(\left(\frac{1}{2}x^2-5y\right)^2\)
7) \(\left(1+3a^2\right)\left(3a^2-1\right)\)
