algebraic expressins 1) $$ -3 a\left(3 a^{2}-6 a^{2}+a\right) $$ 2) $$ \left(2 x^{4}-3 y^{2}\right)\left(3 x^{4}+2 y^{2}\right) $$

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Sure, let's simplify each of the given algebraic expressions step by step.

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### **1) Simplify $$ -3 a\left(3 a^{2} - 6 a^{2} + a\right) $$**

**Step 1: Simplify inside the parentheses**

Combine like terms inside the parentheses:

$$
3a^{2} - 6a^{2} + a = (3 - 6)a^{2} + a = -3a^{2} + a
$$

So, the expression becomes:

$$
-3a(-3a^{2} + a)
$$

**Step 2: Distribute $$-3a$$ across the terms inside the parentheses**

$$
-3a \times (-3a^{2}) + (-3a) \times a = 9a^{3} - 3a^{2}
$$

**Step 3: Write the expression in standard form**

$$
9a^{3} - 3a^{2}
$$

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### **2) Simplify $$ \left(2x^{4} - 3y^{2}\right)\left(3x^{4} + 2y^{2}\right) $$**

**Step 1: Apply the distributive property (FOIL method)**

Multiply each term in the first polynomial by each term in the second polynomial:

$$
\begin{align*}
2x^{4} \times 3x^{4} &= 6x^{8} \
2x^{4} \times 2y^{2} &= 4x^{4}y^{2} \
-3y^{2} \times 3x^{4} &= -9x^{4}y^{2} \
-3y^{2} \times 2y^{2} &= -6y^{4}
\end{align*}
$$

**Step 2: Combine like terms**

$$
6x^{8} + 4x^{4}y^{2} - 9x^{4}y^{2} - 6y^{4}
$$

Combine the $$x^{4}y^{2}$$ terms:

$$
4x^{4}y^{2} - 9x^{4}y^{2} = -5x^{4}y^{2}
$$

**Step 3: Write the simplified expression**

$$
6x^{8} - 5x^{4}y^{2} - 6y^{4}
$$

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**Final Simplified Expressions:**

1. $$ 9a^{3} - 3a^{2} $$

2. $$ 6x^{8} - 5x^{4}y^{2} - 6y^{4} $$
1. $$ 9a^{3} - 3a^{2} $$ 2. $$ 6x^{8} - 5x^{4}y^{2} - 6y^{4} $$

algebraic expressins 1) \( -3 a\left(3 a^{2}-6 a^{2}+a\right) \) 2) \( \left(2 x^{4}-3 y^{2}\right)\left(3 x^{4}+2 y^{2}\right) \)

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