Question

simplify
$(4xy^{2} + 7x - 3x^{3}y) + (x^{3}y - 2y^{2} + 3x)$

Explanation:

Step1: Remove parentheses

To simplify the expression \((4xy^{2}+7x - 3x^{3}y)+(x^{3}y-2y^{2}+3x)\), we first remove the parentheses. Since there is a plus sign in front of both parentheses, the signs of the terms inside remain the same. So we get \(4xy^{2}+7x - 3x^{3}y+x^{3}y-2y^{2}+3x\).

Step2: Combine like terms

• For the \(x^{3}y\) terms: \(-3x^{3}y+x^{3}y=(-3 + 1)x^{3}y=-2x^{3}y\)
• For the \(x\) terms: \(7x+3x=(7 + 3)x = 10x\)
• The terms \(4xy^{2}\) and \(-2y^{2}\) have no like terms to combine with other terms, so they remain as they are.

Putting it all together, we have \(4xy^{2}-2x^{3}y + 10x-2y^{2}\) (we can also rearrange the terms in standard form, but the simplified form with combined like terms is acceptable).

Answer:

\(4xy^{2}-2x^{3}y + 10x-2y^{2}\) (or rearranged as \(-2x^{3}y+4xy^{2}-2y^{2}+10x\))