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(2x+3)(3xy^(2)-2y^(2)+3y)

$(2 x+3)\left(3 x y^{2}-2 y^{2}+3 y\right)$

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Add and subtract polynomials

Full solution

Q.

(2 x+3)\left(3 x y^{2}-2 y^{2}+3 y\right)

Distribute First Term: Distribute the first term of the first expression $2x$ across each term of the second expression. $(2x)(3xy^{2}) + (2x)(-2y^{2}) + (2x)(3y) = 6x^{2}y^{2} - 4xy^{2} + 6xy$
Distribute Second Term: Distribute the second term of the first expression $3$ across each term of the second expression.\(3( $3$ xy^{ $2$ }) + $3$ ( $-2$ y^{ $2$ }) + $3$ ( $3$ y) = $9$ xy^{ $2$ } - $6$ y^{ $2$ } + $9$ y\)
Combine Results: Combine the results from Step $1$ and Step $2$ to get the final expanded expression. $\newline$ $6x^{2}y^{2} - 4xy^{2} + 6xy + 9xy^{2} - 6y^{2} + 9y$
Group and Simplify: Group like terms and simplify the expression. $6x^{2}y^{2} + (9xy^{2} - 4xy^{2}) + 6xy - 6y^{2} + 9y = 6x^{2}y^{2} + 5xy^{2} + 6xy - 6y^{2} + 9y$

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