1. $6a(4c-3b)+15d(4c-3b)$
$(4c-3b)(6a+15d)$
$3(4c-3b)(2a+5d)$
2. $-6\times -5=30$
$-6+-5=-11$
$2x^2-6x-5x+15$
$2x(x-3)-5(x-3)$
$(x-3)(2x-5)$
3. $-5\times -4=20$
$-5+-4=-9$
$5u^2-5uv-4uv+4v^2$
$5u(u-v)-4v(u-v)$
$(u-v)(5u-4v)$
4. $(4x+6y)^2$
5. $-2(x^3-64y^3)$
$-2(x-4y)(x^2+4xy+16y^2)$
6. $20u(v-3u^2)-5x(v-3u^2)$
$(v-3u^2)(20u-5x)$
7. $2(27u^3-8)$
$2(3u-2)(9u^2+6u+4)$
8. $2(27-64x^3)$
$2(3-4x)(9+12x+16x^2)$
9. $n(n-1)$
10. $-25\times 3=-75$
$-25+3=-22$
$5x^2-25x+3x-15$
$5x(x-5)+3(x-5)$
$(x-5)(5x+3)$
11. $x^2-3xy-xy+3y^2$
$x(x-3y)-y(x-3y)$
$(x-3y)(x-y)$
12. $-15\times -15=225$
$-15+-15=-30$
$5(9u^2-30uv+25v^2)$
$5(9u^2-15uv-15uv+25v^2)$
$5(3u(3u-5v)-5v(3u-5v))$
$5(3u-5v)(3u-5v)$
13. $(m-2n)(m+2n)$
14. $3(4ab-6a+2nb-3n)$
$3(2a(2b-3)+n(2b-3))$
$3(2b-3)(2a+n)$
15. $36b^2c-24b^2d+24ac-16ad$
$12b^2(3c-2d)+8a(3c-2d)$
$(3c-2d)(12b^2+8a)$
$4(3c-2d)(3b^2+2a)$
16. $-4\times 2=-8$
$-4+2=-2$
$3m(m^2-2mn-8n^2)$
$3m(m^2-4mn+2mn-8n^2)$
$3m(m(m-4n)+2n(m-4n))$
$3m(m-4n)(m+2n)$
17. $2(64+27x^3)$
$2(4+3x)(16-12x+9x^2)$
18. $(4m+3n)(16m^2-12mn+9n^2)$
19. $5\times 2=10$
$5+2=7$
$n(n^2+7n+10)$
$n(n^2+5n+2n+10)$
$n(n(n+5)+2(n+5))$
$n(n+5)(n+2)$
20. $(4m-n)(16m^2+4mn+n^2)$
21. $(3x-4)(9x^2+12x+16)$
22. $(4a-3b)(4a+3b)$
23. $x(5x+2)$
24. $-6\times -4=24$
$-6+-4=-10$
$2x^2-6x-4x+12$
$2x(x-3)-4(x-3)$
$(x-3)(2x-4)$