Question

SUMA Y RESTA DE TERMINOS SEMEJANTES
A= 3X2y-5Xy2+3
B= -4Xy2+5
C= 8y2x-6yx2
D= 7xy2-5
Realizar con las siguientes propiedades
1 A+B
2 B-C
3 D+C
4 A-B+C
5 3A-2B
6 5C-2D
7 4A+3C
8 A-3B+C
9 B-D+A
10 A+B+C+D

Answer 1

Dados:

$A = {3x}^{2} y - 5x {y}^{2} + 3 \\ B = - 4x {y}^{2} + 5 \\ C = 8x {y}^{2} - 6 {x}^{2} y \\ D = 7x {y}^{2} - 5$

y

Encontraremos las propiedades dadas:

$\quad \quad \quad \quad \quad \: \textbf{A + B } \\ (3 {x}^{2} y - 5x {y}^{2} + 3)\: + ( - 4x {y}^{2} + 5 ) \\ 3 {x}^{2} y - 5x {y}^{2} - 4x {y}^{2} + 3 + 5 \\ \boxed{ \boxed{3 {x}^{2} y - 9x {y}^{2} + 8 }}$

$\quad \quad \quad \quad \quad \quad\textbf{B - C} \\ (-4x {y}^{2} +5) - (8x {y}^{2} - 6 {x}^{2} y) \\ - 4x {y}^{2} + 5 - 8x {y}^{2} + 6 {x}^{2} y \\ 6 {x}^{2} y - 4x {y}^{2} - 8x {y}^{2} + 5 \\ \boxed{ \boxed{6 {x}^{2} y - 12x {y}^{2} + 5}}$

$\quad \quad \quad \quad \quad \quad \textbf{D+C} \\ (7x {y}^{2} - 5) + (8x {y}^{2} - 6 {x}^{2} y) \\ 7x {y}^{2} - 5 + 8x {y}^{2} - 6 {x}^{2} y \\ - 6 {x}^{2} y + 7x {y}^{2} + 8x {y}^{2} - 5 \\ \boxed{ \boxed{ - 6 {x}^{2}y + 15x {y}^{2} - 5}}$

$\quad \quad \quad \quad \quad \textbf{A-B+C} \\ ({3x}^{2} y - 5x {y}^{2} + 3) - (- 4x {y}^{2} + 5) + (8x {y}^{2} - 6 {x}^{2} y) \\ 3 {x}^{2} y - 5x {y}^{2} + 3 + 4x {y}^{2} - 5 + 8x {y}^{2} - 6 {x}^{2} y \\ 3 {x}^{2} y - 6 {x}^{2} y - 5x {y}^{2} + 4x {y}^{2} + 8x {y}^{2} + 3 - 5 \\ \boxed{ \boxed{ - 3 {x}^{2} y + 7x {y}^{2} - 2}}$

$\quad \quad \quad \quad \quad \textbf{3A-2B} \\ 3({3x}^{2} y - 5x {y}^{2} + 3) - 2(- 4x {y}^{2} + 5) \\ 9 {x}^{2} y - 15x {y}^{2} + 9 + 8x {y}^{2} - 10 \\ 9 {x}^{2} y - 15x {y}^{2} + 8x {y}^{2} + 9 - 10 \\ \boxed{ \boxed{9 {x}^{2}y - 7x {y}^{2} - 1 }}$

$\quad \quad \quad \quad \quad \textbf{5C-2D} \\ 5(8x {y}^{2} - 6 {x}^{2} y) - 2(7x {y}^{2} - 5) \\ 40x {y}^{2} - 30 {x}^{2} y - 14x {y}^{2} + 10 \\ - 30 {x}^{2} y + 40x {y}^{2} - 14x {y}^{2} + 10 \\ \boxed{ \boxed{ - 30 {x}^{2} y - 26x {y}^{2} + 10 }}$

$\quad \quad \quad \quad \quad \textbf{4A+3C} \\ 4({3x}^{2} y - 5x {y}^{2} + 3) + 3(8x {y}^{2} - 6 {x}^{2} y) \\ 12 {x}^{2} y - 20x {y}^{2} + 12 + 24x {y}^{2} - 18 {x}^{2} y \\ 12 {x}^{2} y - 18 {x}^{2} y - 20x {y}^{2} + 24x {y}^{2} + 12 \\ \boxed{ \boxed{ - 6 {x}^{2}y + 4x {y}^{2} + 12}}$

$\quad \quad \quad \quad \: \: \textbf{A-3B+C} \\ ( {3x}^{2} y - 5x {y}^{2} + 3) - 3(- 4x {y}^{2} + 5) + (8x {y}^{2} - 6 {x}^{2} y) \\ 3 {x}^{2} y - 5x {y}^{2} + 3 + 12x {y}^{2} - 15 + 8x {y}^{2} - 6 {x}^{2} y \\ 3 {x}^{2} y - 6 {x}^{2}y - 5 x{y}^{2} + 12x {y}^{2} + 8x {y}^{2} + 3 - 15 \\ \boxed{ \boxed{ - 3 {x}^{2} y + 15x {y}^{2} - 12}}$

$\quad \quad \quad \quad \quad \textbf{B-D+A} \\ (- 4x {y}^{2} + 5) - (7x {y}^{2} - 5) + ({3x}^{2} y - 5x {y}^{2} + 3) \\ - 4x {y}^{2} + 5 - 7x {y}^{2} + 5 + 3 {x}^{2} y - 5x {y}^{2} + 3 \\ 3 {x}^{2}y - 4x {y}^{2} - 7x {y}^{2} - 5x {y}^{2} + 5 + 5 + 3 \\ \boxed{ \boxed{3 {x}^{2}y - 16x {y}^{2} + 13 }}$

$\quad \quad \quad \quad \textbf{A+B+C+D} \\ ({3x}^{2} y - 5x {y}^{2} + 3) + (- 4x {y}^{2} + 5) + (8x {y}^{2} - 6 {x}^{2} y) + (7x {y}^{2} - 5) \\ {3x}^{2} y - 5x {y}^{2} + 3 - 4x {y}^{2} + 5 + 8x {y}^{2} - 6 {x}^{2} y - + 7x {y}^{2} - 5 \\ 3 {x}^{2} y - 6 {x}^{2} y - 5x {y}^{2} - 4x {y}^{2} + 8x {y}^{2} + 7x {y}^{2} + 3 + 5 - 5 \\ \boxed{ \boxed{ - 3 {x}^{2}y + 6x {y}^{2} + 3 }}$

Saludos !

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