Polynomial Product E1Cff4

1. **State the problem:** We need to find the product of the two polynomials $2x^4 + 3x^2$ and $x^4 - x^2$. 2. **Formula used:** To multiply two binomials, use the distributive property (also called FOIL for binomials): $$ (a + b)(c + d) = ac + ad + bc + bd $$ 3. **Apply the distributive property:** $$ (2x^4 + 3x^2)(x^4 - x^2) = 2x^4 \cdot x^4 + 2x^4 \cdot (-x^2) + 3x^2 \cdot x^4 + 3x^2 \cdot (-x^2) $$ 4. **Calculate each term:** - $2x^4 \cdot x^4 = 2x^{4+4} = 2x^8$ - $2x^4 \cdot (-x^2) = -2x^{4+2} = -2x^6$ - $3x^2 \cdot x^4 = 3x^{2+4} = 3x^6$ - $3x^2 \cdot (-x^2) = -3x^{2+2} = -3x^4$ 5. **Combine like terms:** $$ 2x^8 + (-2x^6 + 3x^6) - 3x^4 = 2x^8 + (\cancel{-2x^6} + 3x^6) - 3x^4 = 2x^8 + x^6 - 3x^4 $$ 6. **Final answer:** $$ 2x^8 + x^6 - 3x^4 $$ This is the product of the given polynomials.