expand and simplify: (3x + 1)(2 + y)(3 - x)\n3x^{2}y - 8xy + 6x^{2}-16x + 3y - 6\n-3x^{2}y + 8xy…

expand and simplify: (3x + 1)(2 + y)(3 - x)\n3x^{2}y - 8xy + 6x^{2}-16x + 3y - 6\n-3x^{2}y + 8xy - 6x^{2}+16x + 3y + 6\n-3x^{2}y + 10xy - 6x^{2}-20x + 3y - 6\n3x^{2}y + 10xy + 6x^{2}+20x + 3y + 6

expand and simplify: (3x + 1)(2 + y)(3 - x)\n3x^{2}y - 8xy + 6x^{2}-16x + 3y - 6\n-3x^{2}y + 8xy - 6x^{2}+16x + 3y + 6\n-3x^{2}y + 10xy - 6x^{2}-20x + 3y - 6\n3x^{2}y + 10xy + 6x^{2}+20x + 3y + 6

Answer

Explanation:

Step1: Multiply first two binomials

[ \begin{align*} (3x + 1)(2 + y)&=3x\times(2 + y)+1\times(2 + y)\ &=6x+3xy + 2+y \end{align*} ]

Step2: Multiply the result by the third binomial

[ \begin{align*} &(6x+3xy + 2+y)(3 - x)\ &=6x\times(3 - x)+3xy\times(3 - x)+2\times(3 - x)+y\times(3 - x)\ &=18x-6x^{2}+9xy - 3x^{2}y+6 - 2x+3y-xy\ &=- 3x^{2}y+(9xy-xy)-6x^{2}+(18x - 2x)+3y + 6\ &=-3x^{2}y + 8xy-6x^{2}+16x+3y + 6 \end{align*} ]

Answer:

B. $-3x^{2}y + 8xy-6x^{2}+16x+3y + 6$