1: \(7x+7y=7\left(x+y\right)\)
2: \(6x^4-9x^3=3x^3\cdot2x-3x^3\cdot3=3x^3\left(2x-3\right)\)
3: \(5y^{10}+15y^6\)
\(=5y^6\cdot y^4+5y^6\cdot3\)
\(=5y^6\left(y^4+3\right)\)
4: \(2x^2y-6xy^2\)
\(=2xy\cdot x-2xy\cdot3y\)
=2xy(x-3y)
5: \(3x\left(x-1\right)+7x^2\left(x-1\right)\)
\(=\left(x-1\right)\left(7x^2+3x\right)\)
\(=x\left(7x+3\right)\left(x-1\right)\)
6: \(3x\left(x-a\right)+5a\left(a-x\right)\)
=3x(x-a)-5a(x-a)
=(x-a)(3x-5a)
7: \(x^2-6xy+9y^2\)
\(=x^2-2\cdot x\cdot3y+\left(3y\right)^2\)
\(=\left(x-3y\right)^2\)
8: \(x^3-64=x^3-4^3=\left(x-4\right)\left(x^2+4x+16\right)\)
9: \(125x^3+y^6\)
\(=\left(5x\right)^3+\left(y^2\right)^3\)
\(=\left(5x+y^2\right)\left(25x^2-5xy^2+y^4\right)\)
10: \(x^3+6x^2y+12xy^2+8y^3\)
\(=x^3+3\cdot x^2\cdot2y+3\cdot x\cdot\left(2y\right)^2+\left(2y\right)^3\)
\(=\left(x+2y\right)^3\)
11: \(3x^2-12y^2\)
\(=3\left(x^2-4y^2\right)\)
\(=3\left(x-2y\right)\left(x+2y\right)\)
12: \(5xy^2-10xyz+5xz^2\)
\(=5x\left(y^2-2yz+z^2\right)\)
\(=5z\left(y-z\right)^2\)
13: \(\left(2x+1\right)^2-\left(x-1\right)^2\)
\(=\left(2x+1-x+1\right)\left(2x+1+x-1\right)\)
\(=3x\left(x+2\right)\)
14: \(9\left(x+5\right)^2-\left(x-7\right)^2\)
\(=\left(3x+15\right)^2-\left(x-7\right)^2\)
\(=\left(3x+15+x-7\right)\left(3x+15-x+7\right)\)
\(=\left(4x+8\right)\left(2x+22\right)\)
\(=4\cdot\left(x+2\right)\cdot2\left(x+11\right)=8\left(x+2\right)\left(x+11\right)\)
1) 7x+7y=7(x+y)
2) 5y10+156=5y6(y4+3)
3) 3x(x-1)+7x2(x-1)
=(x-1)(3x+7x2)
