1) [tex]6 {y}^{2} - 24y[/tex]
[tex] = > 6y(y - 4)[/tex]
2) [tex]6pq - 4q + 6 - 9p[/tex]
[tex] = > (6pq - 4q) + ( - 9p + 6)[/tex]
[tex] = > [2q(3p - 2)] + [- 3( 3p - 2)] [/tex]
[tex] = > 2q(3p - 2) - 3(3p - 2)[/tex]
[tex] = > (3p - 2)(2q - 3)[/tex]
3) [tex] {x}^{2} + 14xy + 49y[/tex]
[tex] = > {x}^{2} + 2 \times x \times 7y + {(7y)}^{2} [/tex]
[tex] = > {(x + 7y)}^{2} [/tex]
[tex] = > (x + 7y)(x + 7y)[/tex]
4) [tex]25 {y}^{2} - 16[/tex]
[tex] = > {(5y)}^{2} - {4}^{2} [/tex]
[tex] = > (5y + 4)(5y - 4)[/tex]
5) [tex]9 {x}^{2} - 30x + 25[/tex]
[tex] = > {(3x)}^{2} - 2 \times 3x \times 5 + {(5)}^{2} [/tex]
[tex] = > {(3x - 5)}^{2} [/tex]
[tex] = > (3x - 5)(3x - 5)[/tex]
6) [tex] {p}^{2} + 2p - 15[/tex]
[tex] = > {p}^{2} + 5p - 3p - 15[/tex]
[tex] = > p(p + 5) - 3(p + 5)[/tex]
[tex] = > (p + 5)(p - 3)[/tex]
7) [tex] {y}^{2} + 8y + 12 = 0[/tex]
[tex] = > {y}^{2} + 2y + 6y + 12[/tex]
[tex] = > y(y + 2) + 6(y + 2)[/tex]
[tex] = > (y + 2)(y + 6)[/tex]
