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(6x+1)^2+(6x-1)^2-2(1+6x)*(6x-1)
=(6x+1)2-2(6x+1)(6x-1)+(6x-1)2
=[(6x+1)-(6x-1)]2
=(6x+1-6x+1)2
=22
=4
\(\left(6x+1\right)^2+\left(6x-1\right)^2-2\left(1+6x\right)\left(6x-1\right)\)
\(\Rightarrow\left(6x+1\right)^2-2\left(6x+1\right)\left(6x-1\right)+\left(6x-1\right)^2\)
\(\Rightarrow\left(6x+1-6x+1\right)^2\)
\(\Rightarrow2^2\)
\(\Rightarrow4\)
\(\left(6x+1\right)^2+\left(6x-1\right)^2-2\left(1+6x\right)\left(6x-1\right)\)
\(=\left(6x+1-6x+1\right)^2\)
\(=2^2=4\)
\(3\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^2-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)\)
\(=\left(2^{16}-1\right)\left(2^{16}+1\right)\)
\(=2^{32}-1\)
a) \(\left(6x+1\right)^2+\left(6x-1\right)^2-2\left(1+6x\right)\left(6x-1\right)\)
\(=\left(6x+1\right)\left(6x+1\right)+\left(6x-1\right)\left(6x-1\right)-2\left(1+6x\right)\left(6x-1\right)\)
\(=\left(6x+1\right)\left(6x+1\right)+\left(6x-1\right)\left[\left(6x-1\right)-2\left(1+6x\right)\right]\)
\(=\left(6x+1\right)\left(6x+1\right)+\left(6x-1\right)\left(6x-1-2-12x\right)\)
\(=36x^2+12x+1+\left(6x-1\right)\left(-6x-3\right)\)
\(=36x^2+12x+1+\left(-36x^2-12x+3\right)\)
\(=36x^2+12x+1-36x^2-12x+3\)
\(=4\)
\(a,=a^3+3a^2b+3ab^2+b^3-a^3+3a^2b-3ab^2+b^3-2b^3=6a^2b\\ b,=\left(6x+1-6x+1\right)^2=2^2=4\)
$x^4-12x^3+12x^2-12x+111$ tại $x=11$
$=11^4-12\cdot11^3+12\cdot11^2-12\cdot11+111$
$=14641-15972+1452-132+111$
$=100$
$(6x+1)^2+(6x-1)^2-2(1-6x)(6x-1)$
$=(6x+1)^2+(6x-1)^2+2(6x-1)^2$
$=(6x+1)^2+3(6x-1)^2$
$=36x^2+12x+1+3(36x^2-12x+1)$
$=36x^2+12x+1+108x^2-36x+3$
$=144x^2-24x+4$
$=4(36x^2-6x+1)$
b)$3(2^2+1)(2^4+1)(2^8+1)(2^{16}+1)$
$=3\cdot\dfrac{2^4-1}{2^2-1}\cdot\dfrac{2^8-1}{2^4-1}\cdot\dfrac{2^{16}-1}{2^8-1}\cdot\dfrac{2^{32}-1}{2^{16}-1}$
$=3\cdot\dfrac{2^{32}-1}{2^2-1}$
$=3\cdot\dfrac{2^{32}-1}{3}$
$=2^{32}-1$
a) (6x+1)2 + (6x-1)2 - 2(1+6x)(6x-1)
= (6x+1+6x-1)2
=144x2
b) x(2x2 -3) - x2(5x+1) +x2
=2x3 - 3x - 5x3 -x2+x2
=-3x3-3x
=-3x(x2+1)
c) 3(22+1)(24+1)(28+1)(216+1)
= (22-1)(22+1)(24+1)(28+1)(216+1)
= (24-1)(24+1)(28+1)(216+1)
= (28-1)(28+1)(216+1)
= (216-1)(216+1)
= 232 -1
d) 3x(x-2) - 5x(1-x) - 8(x2 -3)
= 3x2-6x - 5x + 5x2 - 8x2 +24
= -11x +24
\(\dfrac{\left(6x+1\right)^2+\left(6x-1\right)^2-2}{\left(1+6x\right)\left(6x-1\right)}=\dfrac{\left(36x^2+12x+1\right)+\left(36x^2-12x+1\right)-2}{\left(6x+1\right)\left(6x-1\right)}=\dfrac{36^2+12x+1+36x^2-12x+1-2}{\left(6x+1\right)\left(6x-1\right)}=\dfrac{72x^2}{\left(6x+1\right)\left(6x-1\right)}\)