\(a^3+4a^2-7a-10\)

\(=\left(a^3+5a^2\right)-\left(a^2+5a\right)-\left(2a+10\right)\)

\(=a^2\left(a+5\right)-a\left(a+5\right)-2\left(a+5\right)\)

\(=\left(a^2-a-2\right)\left(a+5\right)\)

\(=\left(a^2-2a+a-2\right)\left(a+5\right)\)

\(=\left[a\left(a-2\right)+\left(a-2\right)\right]\left(a+5\right)\)

\(=\left(a+1\right)\left(a-2\right)\left(a+5\right)\)

\(a^3+4a^2+4a+3\)

\(=a^3+a^2+3a^2+3a+a+3\)

\(=\left(a^3+a^2+a\right)+\left(3a^2+3a+3\right)\)

\(=a\left(a^2+a+1\right)+3\left(a^2+a+1\right)\)

\(=\left(a+3\right)\left(a^2+a+1\right)\)

4a²b² + 36a²b³ + 6ab⁴

= 2ab²(2a + 18ab + 3b²)

4a²b³ - 6a³b²

= 2a²b²(2b - 3a)

4a²=4b²-4a+1

=(2a)²-2*2a*1+1²-4b²= (2a-1)²-(2b)²(2a-1-2b)(2a-1+2b)

\(4a^2-4a+1-4b^2\)

<=>\(\left(2a-1\right)^2-4b^2\)

<=>\(\left(2a-1+2b\right)\left(2a-1-2b\right)\)

\(4a^2-4a+1-4b^2\)

\(=\left(2a-1\right)^2-4b^2\)

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

 4a^{2 -} 4b² - 4a -1 
= (4a²- 4a +1 ) - 4b²
= [(2a)² -2a.1 + 1² ] - (2b)2
= (2a -1 )² - (2b)2
= 2a - 1 - 2b ) . ( 2a - 1 + 2b )

\(a.25^2-4a^2+12ab-9b^2\\ =25^2-\left(4a^2+12ab-9b^2\right)\\ =25^2-\left(2a-3b\right)^2\\ =\left(25-2a+3b\right)\left(25+2a-3b\right)\\ b.x^3+x^2y-xy^2-y^3\\ =x^2\left(x+y\right)-y^2\left(x+y\right)\\ =\left(x+y\right)\left(x^2-y^2\right)\\ =\left(x+y\right)\left(x+y\right)\left(x-y\right)\\ =\left(x+y\right)^2\left(x-y\right)\)

a: Ta có: \(25x^2-4a^2+12ab-9b^2\)

\(=25x^2-\left(2a-3b\right)^2\)

\(=\left(5x-2a+3b\right)\left(5x+2a-3b\right)\)

b: Ta có: \(x^3+x^2y-xy^2-y^3\)

\(=\left(x-y\right)\left(x^2+xy+y^2\right)+xy\left(x-y\right)\)

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

a2 – b2 – 4a + 4

= a2 – 4a + 4 – b2

= (a – 2)2 – b2

= (a – 2 + b)(a – 2 – b)

= (a + b – 2)(a – b – 2)

4a²b² + 36a²b³ + 6ab⁴

= 2ab²(2a + 18ab + 3b²)

3n(m - 3) + 5m(m - 3)

= (3n + 5m)(m - 3)

2a(x - y) - (y - x)

= (x - y)(2a + 1)

4a²b³ - 6a³b²

= 2a²b²(2b - 3a)