Question

What should be subtracted from 2x³ – 3x²y + 2xy² + 3y² to get x³ – 2x²y + 3xy² + 4y²?

Answer 1

★ $\underline{\underline{\sf{Answer:}}}$  

-x³ + x²y + xy² + y²  

★ $\underline{\underline{\sf{Explanation:}}}$

${\sf 2x^3 - 3x^2y + 2xy^2 + 3y^2 \; from \; x^3 - 2x^2y + 3xy^2 + 4y^2}$

${:\implies \sf x^3 - 2x^2y + 3xy^2 + 4y^2 - (2x^3 - 3x^2y + 2xy^2 + 3y^2)}$

${:\implies \sf x^3 - 2x^2y + 3xy^2 + 4y^2 - 2x^3 + 3x^2y - 2xy^2 - 3y^2}$

${:\implies \sf x^3 - 2x^3 - 2x^2yg + 3x^2y + 3xy^2 - 2xy^2 + 4y^2 - 3y^2}$

${:\implies \sf -x^3 + x^2y + xy^2 + y^2}$

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Answer 2

Step-by-step explanation:

Answer:

-x³ + x²y + xy² + y²

★ \underline{\underline{\sf{Explanation:}}}

Explanation:

{\sf 2x^3 - 3x^2y + 2xy^2 + 3y^2 \; from \; x^3 - 2x^2y + 3xy^2 + 4y^2}2x

3

−3x

2

y+2xy

2

+3y

2

fromx

3

−2x

2

y+3xy

2

+4y

2

{:\implies \sf x^3 - 2x^2y + 3xy^2 + 4y^2 - (2x^3 - 3x^2y + 2xy^2 + 3y^2)}:⟹x

3

−2x

2

y+3xy

2

+4y

2

−(2x

3

−3x

2

y+2xy

2

+3y

2

)

{:\implies \sf x^3 - 2x^2y + 3xy^2 + 4y^2 - 2x^3 + 3x^2y - 2xy^2 - 3y^2}:⟹x

3

−2x

2

y+3xy

2

+4y

2

−2x

3

+3x

2

y−2xy

2

−3y

2

{:\implies \sf x^3 - 2x^3 - 2x^2yg + 3x^2y + 3xy^2 - 2xy^2 + 4y^2 - 3y^2}:⟹x

3

−2x

3

−2x

2

yg+3x

2

y+3xy

2

−2xy

2

+4y

2

−3y

2

{:\implies \sf -x^3 + x^2y + xy^2 + y^2}:⟹−x

3

+x

2

y+xy

2

+y

2