bài 4:
a) (a+1)(a+2)(a2+4)(a-1)(a2+1)(a-2)
=((a+1)(a-1))((a+2)(a-2))(a2+4)(a2+1)
=(a2-1)(a2-4)(a2+4)(a2+1)
=((a2-1)(a2+1))((a2-4)(a2+4))
=(a4-1)(a4-16)
b) (a+2b-3c-d)(a+2b+3c+d)
=(a+2b-(3c+d))(a+2b+3c+d)
=(a+2b)2-(3c+d)2
Bài 4:
a) \(\left(a+1\right)\left(a-1\right)\left(a+2\right)\left(a-2\right)\left(a^2+4\right)\left(a^2+1\right)\)
\(=\left(a^2-1\right)\left(a^2-4\right)\left(a^2+4\right)\left(a^2+1\right)\)
\(=\left(a^4-1\right)\left(a^4-16\right)\)
\(=a^8-17a^4+16\)
b) \(\left(a+2b-3c-d\right)\left(a+2b+3c+d\right)\)
\(=\left(a+2b\right)^2-\left(3c+d\right)^2\)
\(=a^2+4ab+4b^2-9c^2-6cd-d^2\)
c) \(\left(1-x-2x^3+3x^2\right)\left(1-x+2x^3-3x^2\right)\)
\(=\left(1-x\right)^2-\left(2x^3-3x^2\right)^2\)
\(=x^2-2x+1-\left(4x^6-12x^5+9x^4\right)\)
\(=-4x^6+12x^5-9x^4+x^2-2x+1\)
Bài 4:
d) Ta có: \(\left(a^3+3\right)\left(a^6-3a^3+9\right)\)
\(=\left(a^3\right)^3+3^3\)
\(=a^9+27\)
e) Ta có: \(\left(a^2-1\right)\left(a^2-a+1\right)\left(a^2+a+1\right)\)
\(=\left(a-1\right)\left(a^2+a+1\right)\left(a+1\right)\left(a^2-a+1\right)\)
\(=\left(a^3-1\right)\left(a^3+1\right)\)
\(=a^6-1\)
