Question

The sum of two expressions is x square - y square+3y-5, If one of them is 2y square+2x-y-10, find the other.
$the \: sum \: of \: two \: expression \: is \: x {?}^{2} - y {}^{2} + 3y - 5.if \: one \: of \: them \: is \: 2y {}^{2} + 2x - y - 10.find \: the \: other.$
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Answer 1

Answer -

• The other expression is "x² - 3y² + 4y + 5 - 2x".

To find -

• The other expression.

Step-by-step explanation -

• Here, it is given that the sum of two expressions is "x² - y² + 3y - 5" and one of the expressions is "2y² + 2x - y - 10". We have to find the other expression.

Let :-

• The other expression be "z".

Then :-

• The sum of "2y² + 2x - y - 10" and "z" will be "x² - y² + 3y - 5".

Therefore,

➟ (2y² + 2x - y - 10) + (z) = (x² - y² + 3y - 5)

➟ (z) = (x² - y² + 3y - 5) - (2y² + 2x - y - 10)

➟ (z) = x² - y² + 3y - 5 - 2y² - 2x + y + 10

➟ (z) = x² - y² - 2y² + 3y + y - 5 + 10 - 2x

➟ (z) = x² - 3y² + 4y + 5 - 2x

Hence :-

• The other expression is "x² - 3y² + 4y + 5 - 2x".

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V E R I F I C A T I O N

• To check our answer, let's add up x² - 3y² + 4y + 5 - 2x and 2y² + 2x - y - 10 and see whether we get x² - y² + 3y - 5!

⟾ (x² - 3y² + 4y + 5 - 2x) + (2y² + 2x - y - 10)

⟾ x² - 3y² + 4y + 5 - 2x + 2y² + 2x - y - 10

⟾ x² - 3y² + 2y² + 4y - y + 5 - 10 - 2x + 2x

⟾ x² - y² + 3y - 5

We get x² - y² + 3y - 5 on adding up x² - 3y² + 4y + 5 - 2x and 2y² + 2x - y - 10.

Hence verified!!

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Note :- While subtracting algebraic expressions, we change the sign of each term to be subtracted and then add the expressions to get our answer. That's what we did here!