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(a+b)6=a6+6a5b+15a4b2+20a3b3+15a2b4+6ab5+b6
(a+b)7=a7+7a6b+21a5b2+35a4b3+35a3b4+21a2b5+7ab6+b7
(a+b)8=a8+8a7b+28a6b2+56a5b3+70a4b4+56a3b5+28a2b6+8ab7+b8
....
a: \(=\dfrac{2^{36}}{2^{12}}=2^{24}\)
b: \(=3^{18}:\dfrac{3^2}{5^2}=3^{16}\cdot5^2\)
c: \(=-\dfrac{\left(a-b\right)^5}{\left(a-b\right)^3}=-\left(a-b\right)^2\)
d: \(\dfrac{\left(a-b\right)^7}{\left(b-a\right)^4}=\dfrac{\left(a-b\right)^7}{\left(a-b\right)^4}=\left(a-b\right)^3\)
\(1.a\left(a+2b\right)^3-b\left(2a+b\right)^3\)
=\(a\left(a^3+6a^2b+12ab^2+8b^3\right)-b\left(8a^3+12a^2b+6ab^2+b^3\right)\)
=\(a^4+6a^3b+12a^2b^2+8ab^3-8a^3b-12a^2b^2-6ab^3-b^4\)
=\(a^4-b^4\)=\(\left(a^2-b^2\right)\left(a^2+b^2\right)\)
2\
a3+4a2-7a-10
= a3-2a2+6a2-12a+5a-10
=a2(a-2) +6a(a-2) +5(a-2)
= (a-2)(a2+6a+5)
= (a-2)(a+1)(a+5)
4\
(a2+a)2+4(a2+a)-12
= (a2+a)2+4(a2+a)+4-16
= (a2+a+2)2-16
= (a2+a+6)(a2+a-2)
5/
(x2+x+1)(x2+x+2)-12
đặt x2+x+1=a
⇒ a(a+1)-12
= a2+a-12
= a2-3a+4a-12
= a(a-3)+4(a-3)
= (a-3)(a+4)
⇒ (x2+x-2)(x2+x+5)
6\
x8+x+1
= x8+x7+x6-x7-x6-x5+x5+x4+x3-x4-x3-x2+x2+x+1
= x6(x2+x+1) - x5(x2+x+1) +x3(x2+x+1)-x2(x2+x+1)+(x2+x+1)
= (x2+x+1)(x6-x5+x3+x2+1)
7\
x10+x5+1
= x10+x9+x8-x9-x8-x7+x7+x6+x5-x6-x5-x4+x5+x4+x3-x3-x2-x+x2+x+1
= x8(x2+x+1)-x7(x2+x+1)+x5(x2+x+1)-x4(x2+x+1)+x3(x2+x+1)-x(x2+x+1)+(x2+x+1)
= (x2+x+1)(x8-x7+x5-x4+x3-x+1)
1: \(4a^2b^4-c^4d^2\)
\(=\left(2ab^2-c^2d\right)\left(2ab^2+c^2d\right)\)
4: \(\left(a+b\right)^3-\left(a-b\right)^3\)
\(=\left(a+b-a+b\right)\left[\left(a+b\right)^2+\left(a+b\right)\left(a-b\right)+\left(a-b\right)^2\right]\)
\(=2b\left(a^2+2ab+b^2+a^2-b^2+a^2-2ab+b^2\right)\)
\(=2b\left(3a^2+b^2\right)\)
5: \(\left(a+b\right)^3+\left(a-b\right)^3\)
\(=a^3+b^3+3a^2b+3ab^2+a^3-3a^2b+3ab^2-b^3\)
\(=2a^3+6ab^2\)
\(=2a\left(a^2+3b^2\right)\)