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x9 + 1
= (x3)3 + 13
= (x3 + 1)(x6 - x3 + 1)
= (x + 1)(x2 - x + 1)(x6 - x3 +1)
8a3 - 12a2 + 6a - 1
= (2a)3 - 3(2a)21 + 3 . 2a . 12 - 1
= (2a - 1)3
27a3 - 54a2b + 36ab2 - 8b3
= (3a)3 - 3(3a)22b + 3 . 3a . (2b)2 - (2b)3
= (3a - 2b)3
a)\(\left(a^3-b^3\right)+\left(a-b\right)^2\)
\(=\left(a-b\right)\left(a^2+ab+b^2\right)+\left(a-b\right)^2\)
\(\left(a-b\right)\left(a^2+ab+b^2+a-b\right)\)
b) \(\left(8a^3-27b^3\right)-2a\left(4a^2-9b^2\right)\)
\(=\left(2a-3b\right)\left(4a^2+6ab+9b^2\right)-2a\left(2a-3b\right)\left(2a+3b\right)\)
\(=\left(2a-3b\right)\left(4a^2+6ab+9b^2-4a^2-6ab\right)\)
\(=\left(2a-3b\right)\cdot9b^2\)
\(=\left(a-b\right)\left(a^2+ab+b^2\right)+a^2-2ab+b^2\)
= ...........
a) \(4a^3b^3c^2x+12a^3b^4c^2-16a^4b^5cx\)
\(=4a^3b^3c\left(cx+3bc-4ab^2x\right)\)
b) \(\left(b-2c\right)\left(a-b\right)-\left(a+b\right)\left(2c-b\right)\)
\(=\left(b-2c\right)\left(a-b+a+b\right)=2a\left(b-2c\right)\)
c) \(3a\left(a+5\right)-2\left(5+a\right)=\left(a+5\right)\left(3a-2\right)\)
d) \(\left(x+1\right)^2-3\left(x+1\right)=\left(x+1\right)\left(x+1-3\right)\)
\(4a^4b-24a^3b^2+36a^2b^3\)
\(=4a^2b\left(a^2-6ab+9b^2\right)\)
\(=4a^2b\left[a^2-2.a.3b+3b^2\right]\)
\(=4a^2b\left(a-3b\right)^2\)
\(4a^4b-24a^3b^2+36a^2b^3\)
\(=4a^2b\left(a^2-6ab+9b^2\right)\)
\(=4a^2b\left[a^2-2\cdot a\cdot3b+\left(3b\right)^2\right]\)
\(=4a^2b\left(a-3b\right)^2\)
\(x^3+x^2+4=x^3+2x^2-x^2-2x+2x+4\)
\(=x^2\left(x+2\right)-x\left(x+2\right)+2\left(x+2\right)\)
\(=\left(x^2-x+2\right)\left(x+2\right)\)
\(x^8+64=x^8+16x^4+64-16x^4\)
\(=\left(x^4+8\right)^2-\left(4x^2\right)^2\)
\(=\left(x^4-4x^2+8\right)\left(x^4+4x^2+8\right)\)
\(4a^4+b^4=4a^4+4a^2b^2+b^4-4a^2b^2\)
\(=\left(2a^2+b^2\right)^2-\left(2ab\right)^2\)
\(=\left(2a^2+b^2-2ab\right)\left(2a^2+b^2+2ab\right)\)
\(x^3-2x-4=x^3-2x^2+2x^2-4x+2x-4\)
\(=x^2\left(x-2\right)+2x\left(x-2\right)+2\left(x-2\right)\)
\(=\left(x^2+2x+2\right)\left(x-2\right)\)
Chúc bạn học tốt.
8a3b4-12a4b3+4a3b3
=4a3b3.(2b-3a+1)
mình có cảm giác sai sai nếu ai phát hiện nhắc dùm mình nha