Question

(2a+ 3b) ( 3a + 4 b) =
(3x+4y-7)(2X-2y-4)
a+b + c) 2a + 3c - 4 b)

Answer 1

¡Hola!

Problema #1.

$(2a + 3b)(3a + 4b) \\ \\ 2a(3a + 4b) = 6 {a}^{2} + 8ab \\ \\ 3b(3a + 4b) = 9ab + 12 {b}^{2} \\ \\ 6 {a}^{2} + 8ab + 9ab + 12 {b}^{2} \\ \\ \boxed{6 {a}^{2} + 17ab + 12 {b}^{2} }$

Problema #2.

$(3x + 4y - 7)(2x - 2y - 4) \\ \\ 3x(2x - 2y - 4) = 6 {x}^{2} - 6xy - 12x \\ \\ 4y(2x - 2y - 4) = 8xy - 8 {y}^{2} - 16y \\ \\ - 7(2x - 2y - 4) = - 14x + 14y + 28 \\ \\ 6 {x}^{2 } - 8 {y}^{2} + 8xy - 6xy -12x - 14x - 16y + 14y + 28 \\ \\ \boxed{6 {x }^{2} - 8 {y}^{2} + 2xy - 26x- 2y + 28}$

Problema #3.

$(a + b + c)(2a + 3c - 4b) \\ \\ a(2a + 3c - 4b) = 2 {a}^{2} + 3ac - 4ab \\ \\ b(2a + 3c - 4b) = 2ab + 3bc - 4 {b}^{2} \\ \\ c(2a + 3c - 4b) = 2ac + 3 {c}^{2} - 4bc \\ \\ 2 {a}^{2} - 4 {b}^{2} + 3 {c}^{2} + 3ac + 2ac - 4ab + 2ab - 4bc + 3bc \\ \\ \boxed{2 {a}^{2} - 4 {b}^{2} + 3 {c}^{2} + 5ac - 2ab - bc}$

Espero que sirva y saludos.