Simplify the following algebraic expressions: a) (5a2)(4a2) b) (-5xy2)(4x2y3) c) (3x - 2y2z - 3z2) * (2x2yz2)

When multiplying variables with the same base, add their exponents (e.g., $a^m \cdot a^n = a^{m+n}$).

$$a^2 \cdot a^2 = a^{2+2} = a^4$$

$$20a^4$$

The final answer is $\boxed{20a^4}$.

Remember that $x$ is $x^1$.

$$x^1 \cdot x^2 = x^{1+2} = x^3$$

$$-20x^3y^5$$

The final answer is $\boxed{-20x^3y^5}$.

For the first term:

$$(3x)(2x^2yz^2) = (3 \times 2)(x^1 \cdot x^2)(y)(z^2) = 6x^{1+2}yz^2 = 6x^3yz^2$$

For the second term:

$$-(2y^2z)(2x^2yz^2) = -(2 \times 2)(x^2)(y^2 \cdot y^1)(z^1 \cdot z^2) = -4x^2y^{2+1}z^{1+2} = -4x^2y^3z^3$$

For the third term:

$$-(3z^2)(2x^2yz^2) = -(3 \times 2)(x^2)(y)(z^2 \cdot z^2) = -6x^2yz^{2+2} = -6x^2yz^4$$

$$6x^3yz^2 - 4x^2y^3z^3 - 6x^2yz^4$$

The final answer is $\boxed{6x^3yz^2 - 4x^2y^3z^3 - 6x^2yz^4}$.

Question One: Simplify the following

1. $7(5a^2b + 7x - 2a^2b)$

The like terms are $5a^2b$ and $-2a^2b$.

$$5a^2b - 2a^2b = (5-2)a^2b = 3a^2b$$

So the expression inside the parenthesis becomes:

$$(3a^2b + 7x)$$

$$21a^2b + 49x$$

The final answer is $\boxed{21a^2b + 49x}$.

2. $-6y(p^2 - 3y + 7 - 5y)$

The like terms are $-3y$ and $-5y$.

$$-3y - 5y = (-3-5)y = -8y$$

So the expression inside the parenthesis becomes:

$$(p^2 - 8y + 7)$$

$$-6y(p^2) = -6p^2y$$ $$-6y(-8y) = (-6 \times -8)(y \cdot y) = 48y^2$$ $$-6y(7) = -42y$$

$$-6p^2y + 48y^2 - 42y$$

The final answer is $\boxed{-6p^2y + 48y^2 - 42y}$.