Question

1. Solve the following problems.​

Answer 1

Answer:

Question 1:-

${x}^{3} + 5 {x}^{2} + 3x + ( {6x}^{2} - 8 {x}^{3} + 8)$

${x}^{3} + 5 {x}^{2} + 3x + {6x}^{2} - 8 {x}^{3} + 8$

${x}^{3} - 8 {x}^{3} + 5 {x}^{2} + 6 {x}^{2} + 3x + 8$

$= \: \: - 7 {x}^{3} + 11 {x}^{2} + 3x + 8$

Question 2:-

${x}^{3} - 2x {y}^{2} + 5 {x}^{2} y - 6 \: \: from \: \: {x}^{3} + 3 {x}^{2} y + 3x {y}^{2} - 2$

$= {x}^{3} + 3 {x}^{2} y + 3x {y}^{2} - 2- ( {x}^{3} - 2x {y}^{2} + 5 {x}^{2} y + 3x {y}^{2} - 6)$

$= {x}^{3} + 3 {x}^{2} y + 3x {y}^{2} - 2 - {x}^{3} + 2x {y}^{2} - 5 {x}^{2} y - 3x {y}^{2} + 6$

$= {x}^{3} - {x}^{3} + 3 {x}^{2} y - 5 {x}^{2} y-2 + 3x {y}^{2} - 3x {y}^{2} + 6$

$= \: - 2 {x}^{2} y + 4$

Concept:-

• In addition just add the like terms.
• In subtraction from comes first and subtract the like terms.

Answer 2

Answer:

${\large{\underline{\sf{Solution \big \{1 \big \}-}}}}$

${ \longrightarrow{ \sf{ {x}^{3} + 5 {x}^{2} + 3x + (6 {x}^{2} - 8 {x}^{3} + 8)}}}$

${ \longrightarrow{ \sf{ {x}^{3} + 5 {x}^{2} + 3x + 6 {x}^{2} - 8 {x}^{3} + 8}}}$

${ \longrightarrow{ \sf{ {x}^{3} - 8 {x}^{3} + 5 {x}^{2} + 6 {x}^{2} + 3x + 8}}}$

${ \longrightarrow{ \sf{ - 7 {x}^{3} + 11 {x}^{2} + 3x + 8 }}}$

${ \therefore{ \underline{ \rm{ \pmb{ \pink{ The \: Required \: Answer \: is \: - 7 {x}^{3} + 11 {x}^{2} + 3x + 8 }}}}}}$

${\large{\underline{\sf{Solution \big \{2 \big \}-}}}}$

${ \longrightarrow{ \sf{ {x}^{3} + 3 {x}^{2}y + 3 x {y}^{2} - 2- ( {x}^{3} - 2 x {y}^{2} + 5 {x}^{2} y - 6) }}}$

${ \longrightarrow{ \sf{ {x}^{3} + 3 {x}^{2}y + 3 x {y}^{2} - 2- {x}^{3} + 2 x {y}^{2} - 5 {x}^{2} y + 6}}}$

${ \longrightarrow{ \sf{ {x}^{3} - {x}^{3} + 3 {x}^{2}y - 5 {x}^{2}y + 3 x {y}^{2} + 2x {y}^{2} - 2 + 6 }}}$

${ \longrightarrow{ \sf{ - 2 {x}^{2}y + 5x {y}^{2} + 4 }}}$

${ \therefore{ \underline{ \rm{ \pmb{ \pink{ The \: Required \: Answer \: is \: - 2 {x}^{2}y + 5x {y}^{2} + 4 }}}}}}$