Question

# What must be subtracted from 3x^{2}-5xy -2y^{2}-3 to get 5x^{2}-7xy -3y^{2}+3x

Hint:

### Subtraction of polynomials.

○ Always take like terms together while performing subtraction.

○ In addition to polynomials only terms with the same coefficient are subtracted.

## The correct answer is: Hence, the other term must subtract is - 2x2 + y2 + 2xy - 3x - 3.

### Answer:

Step by step explanation:

○ Given:

Terms:

3x^{2}-5xy -2y^{2}-3

5x^{2}-7xy -3y^{2}+3x

○ Step 1:

○ Let A must be subtracted from 3x^{2}-5xy -2y^{2}-3 to get 5x^{2}-7xy -3y^{2}+3x.

So,

3x^{2}-5xy -2y^{2}-3 - A = 5x^{2}-7xy -3y^{2}+3x

A = (3x^{2}-5xy -2y^{2}-3) - ( 5x^{2}-7xy -3y^{2}+3x )

A = 3x^{2}-5xy -2y^{2}- 3- 5x^{2 }+ 7xy + 3y^{2 }- 3x

A = 3x^{2 }- 5x^{2 }+ 3y^{2 }-2y^{2 }-5xy + 7xy - 3x - 3

A = - 2x^{2 }+ y^{2 }+ 2xy - 3x - 3

A = - 2x^{2 }+ y^{2 }+ 2xy - 3x - 3.

- Final Answer:

Hence, the other term must subtract is - 2x^{2 }+ y^{2 }+ 2xy - 3x - 3.

^{2}-5xy -2y

^{2}-3

^{2}-7xy -3y

^{2}+3x

○ Step 1:

○ Let A must be subtracted from 3x

^{2}-5xy -2y

^{2}-3 to get 5x

^{2}-7xy -3y

^{2}+3x.

So,

^{2}-5xy -2y

^{2}-3 - A = 5x

^{2}-7xy -3y

^{2}+3x

^{2}-5xy -2y

^{2}-3) - ( 5x

^{2}-7xy -3y

^{2}+3x )

^{2}-5xy -2y

^{2}- 3- 5x

^{2 }+ 7xy + 3y

^{2 }- 3x

^{2 }- 5x

^{2 }+ 3y

^{2 }-2y

^{2 }-5xy + 7xy - 3x - 3

^{2 }+ y

^{2 }+ 2xy - 3x - 3

^{2 }+ y

^{2 }+ 2xy - 3x - 3.

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