Add x2-2 x y-y2 to the sum of x2-3 y2 and 2 x2-y2-9

Sum of x2 3y2 and 2x2 y2 + 9 = (x2 3y2) + (2x2 y2 + 9) = x2 + 2x2 3y2 y2+ 9 = 3x2 4y2 + 9 Now, required expression = (x2 + 2xy + y2) + (3x2 4y2 ...

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Byju's Answer

Standard VII

Mathematics

Addition of Algebraic Expressions

Add x2+2 x y+...

Question

Add x² + 2xy + y² to the sum of x² − 3y² and 2x² − y²+ 9.

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Solution

Sum of x² - 3y² and 2x² - y² + 9
= (x² - 3y²) + (2x² - y² + 9)
= x² + 2x² - 3y² - y²+ 9
= 3x² - 4y² + 9

Now, required expression = (x² + 2xy + y²) + (3x² - 4y² + 9)
= x² + 3x² + 2xy + y² - 4y² + 9
= 4x² + 2xy - 3y²+ 9

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Add x2 + 2xy + y2 to the sum of x2 − 3y2 and 2x2 − y2+ 9.

Sum of x2 - 3y2 and 2x2 - y2 + 9 = (x2 - 3y2) + (2x2 - y2 + 9) = x2 + 2x2 - 3y2 - y2+ 9 = 3x2 - 4y2 + 9 Now, required expression = (x2 + 2xy + y2) + (3x2 - 4y2 + 9) = x2 + 3x2 + 2xy + y2 - 4y2 + 9 = 4x2 + 2xy - 3y2 + 9

Add x² + 2xy + y² to the sum of x² − 3y² and 2x² − y²+ 9.

Sum of x² - 3y² and 2x² - y² + 9
= (x² - 3y²) + (2x² - y² + 9)
= x² + 2x² - 3y² - y²+ 9
= 3x² - 4y² + 9

Now, required expression = (x² + 2xy + y²) + (3x² - 4y² + 9)
= x² + 3x² + 2xy + y² - 4y² + 9
= 4x² + 2xy - 3y²+ 9