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Question

Add: $$(4x^2-7xy+4y^2-3), (5+6y^2-8xy+x^2)$$ and $$(6-2xy+2x^2-5y^2)$$.


Solution

Let us add the given expressions $$4x^2−7xy+4y^2−3,5+6y^2−8xy+x^2 $$ and $$6−2xy+2x^2−5y^2$$ as shown below:

$$(4x^{ 2 }−7xy+4y^{ 2 }−3)+(5+6y^{ 2 }−8xy+x^{ 2 })+(6−2xy+2x^{ 2 }−5y^{ 2 })\\ =4x^{ 2 }−7xy+4y^{ 2 }−3+5+6y^{ 2 }−8xy+x^{ 2 }+6−2xy+2x^{ 2 }−5y^{ 2 }\\ =(4x^{ 2 }+x^{ 2 }+2x^{ 2 })+(−7xy−8xy−2xy)+(4y^{ 2 }+6y^{ 2 }-5y^{ 2 })+(-3+5+6)\quad \quad \quad (Combining\quad like\quad terms)\\ =(4+1+2)x^{ 2 }+(-7-8-2)xy+(4+6-5)y^{ 2 }+8\\ =7x^{ 2 }-17xy+5y^{ 2 }+8$$

Hence, $$(4x^{ 2 }−7xy+4y^{ 2 }−3)+(5+6y^{ 2 }−8xy+x^{ 2 })+(6−2xy+2x^{ 2 }−5y^{ 2 })=7x^{ 2 }-17xy+5y^{ 2 }+8$$.

Mathematics

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