Fully simplify each of the foll i. $$ (2 x+y)\left(3 x^{2}+2 x y+5 y^{2}\right) $$

Question

UpStudy AI · Accepted Answer

To fully simplify the expression:

$$
(2x + y)\left(3x^{2} + 2xy + 5y^{2}\right)
$$

**Step 1: Distribute each term in the first binomial to each term in the second polynomial.**

$$
= 2x \cdot 3x^{2} + 2x \cdot 2xy + 2x \cdot 5y^{2} + y \cdot 3x^{2} + y \cdot 2xy + y \cdot 5y^{2}
$$

**Step 2: Perform the multiplication for each term.**

$$
= 6x^{3} + 4x^{2}y + 10xy^{2} + 3x^{2}y + 2xy^{2} + 5y^{3}
$$

**Step 3: Combine like terms.**

- Combine $$x^{2}y$$ terms:
  $$
  4x^{2}y + 3x^{2}y = 7x^{2}y
  $$
  
- Combine $$xy^{2}$$ terms:
  $$
  10xy^{2} + 2xy^{2} = 12xy^{2}
  $$

**Step 4: Write the simplified expression.**

$$
6x^{3} + 7x^{2}y + 12xy^{2} + 5y^{3}
$$

**Final Answer:**

$$
6x^{3} + 7x^{2}y + 12xy^{2} + 5y^{3}
$$
$$6x^{3} + 7x^{2}y + 12xy^{2} + 5y^{3}$$

Fully simplify each of the foll
i.