Questions: Find the product. [ left(x^2+5right)left(x^4-3right) ] [ left(x^2+5right)left(x^4-3right)= ]

Transcript text: MyLab Math Homework Do Homework - HW \#30 - ML -- mylab.pearson.com/Student/PlayerHomework.aspx?homeworkId=680333859\&questionld=8 Beginning Algebra (MATH-0950-WBP04) ework: HW \#30 - Multiplying Polynomials and the ributive Property on list Find the product. \[ \left(x^{2}+5\right)\left(x^{4}-3\right) \] tion 7 \[ \left(x^{2}+5\right)\left(x^{4}-3\right)= \] $\square$

Solution

Solution Steps

To find the product of two polynomials, we will use the distributive property. This involves multiplying each term in the first polynomial by each term in the second polynomial and then combining like terms.

Step 1: Define the Polynomials

We start with the two polynomials: \[ \text{poly1} = x^{2} + 5 \] \[ \text{poly2} = x^{4} - 3 \]

Step 2: Apply the Distributive Property

To find the product of the two polynomials, we apply the distributive property: \[ (x^{2} + 5)(x^{4} - 3) = x^{2} \cdot x^{4} + x^{2} \cdot (-3) + 5 \cdot x^{4} + 5 \cdot (-3) \]

Step 3: Simplify the Expression

Calculating each term, we have: \[ x^{2} \cdot x^{4} = x^{6} \] \[ x^{2} \cdot (-3) = -3x^{2} \] \[ 5 \cdot x^{4} = 5x^{4} \] \[ 5 \cdot (-3) = -15 \] Combining these results, we get: \[ x^{6} + 5x^{4} - 3x^{2} - 15 \]