(b+a)^2*(b^2-2*a*b+a^2+4)

\(=\left[a^2+b^2+2-2\left(ab-1\right)\right]\left[a^2+b^2+2+2\left(ab-1\right)\right]\\ =\left(a^2+b^2-2ab+4\right)\left(a^2+b^2+2ab\right)\\ =\left(a+b\right)^2\left(a^2+b^2-2ab+4\right)\)

\(\left(a^2+b^2+2\right)^2-\left(2ab-2\right)^2\)

\(=\left(a^2+b^2+2-2ab+2\right)\left(a^2+b^2+2+2ab-2\right)\)

\(=\left(a^2+b^2-2ab+4\right)\left(a+b\right)^2\)

\(abc-\left(ab+bc+ac\right)+\left(a+b+c\right)-1=\left(abc-ab\right)-\left(bc-b\right)-\left(ac-a\right)+\left(c-1\right)=ab\left(c-1\right)-b\left(c-1\right)-a\left(c-1\right)+\left(c-1\right)=\left(c-1\right)\left(ab-b-a+1\right)=\left(c-1\right)\left[b\left(a-1\right)-\left(a-1\right)\right]=\left(a-1\right)\left(b-1\right)\left(c-1\right)\)

=abc-ab-bc-ca+a+b+c-1

=(abc-bc)-(ca-c)-(ab-b)+(a-1)

=bc(a-1)-c(a-1)-b(a-1)+(a-1)

=(a-1)(bc-c-b+1)

=(a-1)(c(b-1)-(b-1))

=(a-1)(b-1)(c-1)

(a+b)³+(a-b)³=(a³+3a²b+3ab²+b³)+(a³-3a²b+3ab²-b³)

                   =a⁶+6a²b⁴

b) \(a^6-b^3\)

\(=\left(a^2\right)^3-b^3\)

\(=\left(a^2-b\right)\left(a^4+a^2b+b^2\right)\)

c) \(x^4-1\)

\(=\left(x^2\right)^2-1^2\)

\(=\left(x^2-1\right)\left(x^2+1\right)\)

\(=\left(x-1\right)\left(x+1\right)\left(x^2+1\right)\)

\(=4ab\left(ab+ax+bx+x^2\right)=4a^2b^2+4a^2bx+4ab^2x+4abx^2\)

4ab(a + x)(b + x) là nhân tử rồi nhé

\(\left(ab-1\right)^2+\left(a+b\right)^2=a^2b^2-2ab+1+a^2+2ab+b^2=a^2+b^2+a^2b^2+1=a^2\left(b^2+1\right)+\left(b^2+1\right)=\left(a^2+1\right)\left(b^2+1\right)\)

\(\left(ab-1\right)^2+\left(a+b\right)^2=a^2b^2-2ab+1+a^2+2ab+b^2=a^2b^2+a^2+b^2+1=\left(a^2b^2+a^2\right)+\left(b^2+1\right)=a^2\left(b^2+1\right)+\left(b^2+1\right)=\left(a^2+1\right)\left(b^2+1\right)\)

\(\left(ab-1\right)^2+\left(a+b\right)^2\)

\(=a^2b^2+1+a^2+b^2\)

\(=\left(a^2+1\right)\left(b^2+1\right)\)

\(B=a\left(b^2-c^2\right)+b\left(c^2-a^2\right)+c\left(a^2-b^2\right)\)

\(B=ab^2-ac^2+bc^2-a^2b+a^2c-b^2c\)

\(B=\left(ab^2-a^2b\right)-\left(ac^2-c^2b\right)+\left(a^2c-b^2c\right)\)

\(B=-ab\left(a-b\right)-c^2\left(a-b\right)+c\left(a-b\right)\left(a+b\right)\)

\(B=\left(a-b\right)\left(-ab-c^2+ac+bc\right)\)

\(B=\left(a-b\right)\left[a\left(c-b\right)-c\left(c-b\right)\right]\)

\(B=\left(a-b\right)\left(c-b\right)\left(a-c\right)\)

\(x^2-xy\left(a+b\right)+aby^2=x^2-xya-xyb+aby^2=x\left(x-ya\right)-yb\left(x-ya\right)=\left(x-ya\right)\left(x-yb\right)\)

\(x^2-xy\left(a+b\right)+aby^2\)

\(=x^2-axy-bxy+aby^2\)

\(=x\left(x-ay\right)-by\left(x-ay\right)\)

\(=\left(x-ay\right)\left(x-by\right)\)