Questions: What is the product of the 2x^3 and the 4x^2y-3xy^2? a.) 8x^5y-3xy^2 b.) 8x^6y-3xy^2 c.) 8x^6y-6x^3y^2 d.) 8x^5y-6x^4y^2

Transcript text: What is the product of the $2 x^{3}$ and the $4 x^{2} y-3 x y^{2} ?$ a.) $8 x^{5} y-3 x y^{2}$ b.) $8 x^{6} y-3 x y^{2}$ c.) $8 x^{6} y-6 x^{3} y^{2}$ d.) $8 x^{5} y-6 x^{4} y^{2}$

Solution

Solution Steps

Step 1: Multiply the monomial $a x^n$ by the first term of the binomial $b x^m y^p$

We apply the distributive property to get: $a \cdot b \cdot x^{n+m} \cdot y^p = 8x^{n+m}y^p = 8x^{5}y^{1}$

Step 2: Multiply the monomial $a x^n$ by the second term of the binomial $c x^q y^r$

We apply the distributive property to get: $a \cdot c \cdot x^{n+q} \cdot y^r = -6x^{n+q}y^r = -6x^{4}y^{2}$

Final Answer:

The product of the monomial and binomial is: $8x^{5}y^{1} - 6x^{4}y^{2}$

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