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**Addition of algebraic expressions**

To add algebraic expressions, rearrange the terms in the sum of the given algebraic expressions, so that their like terms and constants are grouped together. While rearranging terms, move them with the correct plus (+) or minus (â€“) sign before them.

To add like terms in an algebraic expression, multiply the sum of their coefficients with their common algebraic factors.

e.g. Add 5x^{2}y + 6 and 2x^{2}y â€“ 11.

Sol: (5x^{2}y + 6) + (2x^{2}y â€“ 11)

= 5x^{2}y + 6 + 2x^{2}y â€“ 11

= 5x^{2}y + 2x^{2}y + 6 â€“ 11

= (5 + 2)x^{2}y + 6 â€“ 11

= 7x^{2}y â€“ 5.

**Subtraction of algebraic expressions**

To subtract algebraic expressions

- Change the signs of the terms of the expression being subtracted.
- Rearrange the terms in the difference of the given algebraic expressions, so that their like terms and constants are grouped together.
- While rearranging terms, move them with the correct signs before them.
- Multiply the difference of their coefficients with their common algebraic factors.
- Unlike terms remain unchanged in the sum or difference of algebraic expressions.

e.g. Subtract 2xy â€“ 3x ^{2}y â€“ 4 from 2x^{2}y â€“ 3xy + 4y + 5.

= (2x^{2}y â€“ 3xy + 4y + 5) â€“ (2xy â€“ 3x^{2}y â€“ 4)

= 2x^{2}y â€“ 3xy + 4y + 5 â€“ 2xy + 3x^{2}y + 4

= 2x^{2 }y + 3x^{2}y â€“ 3xy â€“ 2xy + 4y + 5 + 4

= (2 + 3)x^{2}y â€“ 3xy â€“ 2xy + 4y + 5 + 4

= 5x^{2 }y â€“ 5xy + 4y + 9.

**Addition of algebraic expressions**

To add algebraic expressions, rearrange the terms in the sum of the given algebraic expressions, so that their like terms and constants are grouped together. While rearranging terms, move them with the correct plus (+) or minus (â€“) sign before them.

To add like terms in an algebraic expression, multiply the sum of their coefficients with their common algebraic factors.

e.g. Add 5x^{2}y + 6 and 2x^{2}y â€“ 11.

Sol: (5x^{2}y + 6) + (2x^{2}y â€“ 11)

= 5x^{2}y + 6 + 2x^{2}y â€“ 11

= 5x^{2}y + 2x^{2}y + 6 â€“ 11

= (5 + 2)x^{2}y + 6 â€“ 11

= 7x^{2}y â€“ 5.

**Subtraction of algebraic expressions**

To subtract algebraic expressions

- Change the signs of the terms of the expression being subtracted.
- Rearrange the terms in the difference of the given algebraic expressions, so that their like terms and constants are grouped together.
- While rearranging terms, move them with the correct signs before them.
- Multiply the difference of their coefficients with their common algebraic factors.
- Unlike terms remain unchanged in the sum or difference of algebraic expressions.

e.g. Subtract 2xy â€“ 3x ^{2}y â€“ 4 from 2x^{2}y â€“ 3xy + 4y + 5.

= (2x^{2}y â€“ 3xy + 4y + 5) â€“ (2xy â€“ 3x^{2}y â€“ 4)

= 2x^{2}y â€“ 3xy + 4y + 5 â€“ 2xy + 3x^{2}y + 4

= 2x^{2 }y + 3x^{2}y â€“ 3xy â€“ 2xy + 4y + 5 + 4

= (2 + 3)x^{2}y â€“ 3xy â€“ 2xy + 4y + 5 + 4

= 5x^{2 }y â€“ 5xy + 4y + 9.