a ) \(VT=\left(2x+3\right)\left(4x^2+9\right)\left(2x-3\right)\)
\(=\left[\left(2x+3\right)\left(2x-3\right)\right]\left(4x^2+9\right)\)
\(=\left(4x^2-9\right)\left(4x^2+9\right)\)
\(=16x^4-81=VP\left(đpcm\right)\)
b ) \(VT=\left(a+b\right)^2+2\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\)
\(=\left(a+b+a-b\right)^2\)
\(=\left(2a\right)^2=4a^2=VP\left(đpcm\right)\)
Chứng minh các đẳng thức sau:
a) \(\left(a+b+c\right)^2+\left(b+c-a\right)^2+\left(a+c-b\right)^2+\left(a+b-c\right)^2=4\left(a^2+b^2+c^2\right)\)
b) \(\left(a+b+c\right)^3-\left(b+c-a\right)^3-\left(c+a-b\right)^3-\left(a+b-c\right)^3=24abc\)
1) Tìm x biết,
\(4\left(x+1\right)^2+\left(2x-1\right)^2-8\left(x-1\right)\left(x+1\right)=11\)
2) Rút gọn các biểu thức
a) \(2x\left(2x-1\right)^2-3x\left(x+3\right)\left(x-3\right)-4x\left(x+1\right)^2\)
b) \(\left(a-b+c\right)^2-\left(b-c\right)^2+2ab-2ac\)
c) \(\left(3x+1\right)^2-2\left(3x+1\right)\left(3x+5\right)+\left(3x+5\right)^2\)
d) \(\left(3+1\right)\left(3^2+1\right)\left(3^4+1\right)\left(3^8+1\right)\left(3^{16}+1\right)\left(3^{32}+1\right)\)
e) \(\left(a+b-c\right)^2+\left(a-b+c\right)^2-2\left(b-c\right)^2\)
3) Chứng minh rằng các biểu thức sau luôn luôn có giá trị dương với mọi giá trị của biến
a) \(9x^2-6x+2\)
b) \(x^2+x+1\)
c) \(2x^2+2x+1\)
4) Tìm GTNN của các biểu thức
a) A=\(x^2-3x+5\)
b) B=\(\left(2x-1\right)^2+\left(x+2\right)^2\)
GIÚP MK VỚI!!!!!!!!!!
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) \(\left(2x-1\right)^2+\left(x+3\right)^2-5\left(x-7\right)\left(x+7\right)=0\)
Bài 1: Tìm x
a) \(\left(5-2x\right)^2-16=0\)
b) \(x^2-4x=29\)
c) \(\left(x-3\right)^3-\left(x-3\right).\left(x^2+3x+9\right)+9.\left(x+1\right)^2=15\)
d) \(2.\left(x-5\right).\left(x+5\right)-\left(x+2\right).\left(2x-3\right)+x.\left(x^2-8\right)=\left(x+1\right).\left(x^2-x+1\right)\)
Bài 2: Rút gọn
a) \(\left(x^2+x+1\right).\left(x^2-x+1\right).\left(x^2-1\right)\)
b) \(\left(a+b-c\right)^2+\left(a-b+c\right)^2-2.\left(b-c\right)^2\)
c) \(\left(a+b+c\right)^2-\left(a+b\right)^2-\left(a+c\right)^2-\left(b+c\right)^2\)
d) \(\left(a+b+c\right)^2+\left(a-b-c\right)^2+\left(b-c-a\right)^2+\left(c-a-b\right)^2\)
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) \(\left(5+3\right)\left(5^2+3^2\right)\left(5^4+3^4\right)...\left(5^{\text{64}}+3^{64}\right)+\dfrac{5^{128}-3^{128}}{2}\)
Rút gọn các biểu thức sau :
a) \(\left(x^2-2x+2\right)\left(x^2-2\right)\left(x^2+2x+2\right)\left(x^2+2\right)\)
b) \(\left(x+1\right)^3+\left(x-1\right)^3-x^3-3x\left(x+1\right)\left(x-1\right)\)
c) \(\left(a+b+c\right)^2+\left(a+b-c\right)^2+\left(2a-b\right)^2\)
d) \(100^2-99^2+98^2+97^2+......+2^2-1^2\)
e) \(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)+...+\left(2^{64}+1\right)+1\)
f) \(\left(a+b+c\right)^{^{ }2}+\left(a+b-c\right)^2-2\left(a+b\right)^2\)
Chứng minh các biểu thức sau
a) \(\left(a^2-1\right)^2+4a^2=\left(a^2+1\right)^2\)
b) \(\left(x-y\right)^2+\left(x+y\right)^2+2\left(x^2-y^2\right)=4x^2\)
Chứng minh biểu thức sau không phụ thuộc vào biến.
\(1,\left(2x+3\right).\left(4x^2-6x+9\right)-2.\left(4x^3-1\right)\)
\(2,\left(4x-1\right)^3-\left(4x-3\right).\left(16x^2+3\right)\)
\(3,\left(x+1\right)^3-\left(x-1\right)^3-6.\left(x+1\right).\left(x-1\right)\)
Chứng minh các hằng đẳng thức sau:
a) \(\left(ax+yy+cz\right)^2+\left(bx-ay\right)^2+\left(cy-bz\right)^2+\left(az-cx\right)^2=\left(a^2+b^2+c^2\right)\left(x^2+y^2+z^2\right)\)
b) \(\left(ab+bc+ac\right)^2+\left(a^2-bc\right)+\left(b^2-ca\right)^2+\left(c^2-ab\right)^2=\left(a^2+b^2+c^2\right)^2\)
