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a, Sửa đề :
\(a^2+b^2-ac+2ab-bc\)
\(=\left(a+b\right)^2-c\left(a+b\right)=\left(a+b\right)\left(a+b-c\right)\)
b, \(\frac{1}{4}a^2b-bc^4=b\left(\frac{1}{4}a^2-c^4\right)=b\left(\frac{1}{2}a-c^2\right)\left(\frac{1}{2}a+c^2\right)\)
a/ 3(a + b) + c(a + b) = (a + b)(3 + c)
b/ (a - b)2 - c2 = (a - b - c)(a - b + c)
\(25-a^2+2ab-b^2\)
\(=25-\left(a^2-2ab+b^2\right)\)
\(=5^2-\left(a-b\right)^2\)
\(=\left(5-a+b\right)\left(5+a-b\right)\)
a) =a(b2- c2) + bc2- ba2 +a2c - b2c
=a(b2-c2) - (b2c - bc2) - (ba2 - a2c)
=a(b-c)(b+c) -bc(b-c) - a2(b-c)
=(b-c)\(\left[a\left(b+c\right)-bc-a^2\right]\)
=(b-c)(ab+ac-bc-a2)
=\(\left(b-c\right)\left[\left(ab-bc\right)-\left(a^2-ac\right)\right]\)
=\(\left(b-c\right)\left[b\left(a-c\right)-a\left(a-c\right)\right]\)
=\(\left(b-c\right)\left(a-c\right)\left(b-a\right)\)
\(a^3b-ab^3+a^2+2ab+b^2\)
\(=\left(a^3b-ab^3\right)+\left(a^2+2ab+b^2\right)\)
\(=ab\left(a^2-b^2\right)+\left(a+b\right)^2\)
\(=ab\left(a-b\right)\left(a+b\right)+\left(a+b\right)^2\)
\(=\left(a+b\right)\left[ab\left(a-b\right)+\left(a+b\right)\right]\)
\(=\left(a+b\right)\left(a^2b-ab^2+a+b\right)\)
a^2 + b^2 - 2a + 2b - 2ab
= (a^2 - 2ab + b^2) - 2(a - b)
= (a - b)^2 - 2(a - b)
= (a - b)(a - b - 2)
a^2+b^2-2a+2b-2ab
=(a^2+b^2-2ab)-(2a-2b)
=(a-b)^2-2(a-b)
=(a-b)(a-b-2)
\(ab\left(x^2-y^2\right)-xy\left(a^2-b^2\right)\)
\(=abx^2-aby^2-xya^2+b^2xy\)
\(=\left(abx^2-xya^2\right)+\left(b^2xy-aby^2\right)\)
\(=ax\left(bx-ay\right)+by\left(bx-ay\right)\)
\(=\left(ax+by\right)\left(bx-ay\right)\)
a2+2ab+b2-ac-bc
=(a+b)2-c.(a+b)
=(a+b)(a+b-c)