Question18. $a^{2} b-b^{3}$
19. $-98+2 x^{2}$

STEP 1

1. The expressions given are algebraic and involve basic operations such as exponentiation, multiplication, and addition/subtraction.
2. The problems might require simplification or solving for a variable.
_HIGH_LEVEL_APPROACH_ for Problem 18:
1. Identify and factor common terms if possible.
_HIGH_LEVEL_APPROACH_ for Problem 19:
1. Identify and simplify the expression if possible.
2. Consider solving for $x$ if required.
### Problem 18: $a^{2} b - b^{3}$

STEP 2

STEP 3

Identify if there is a common factor in the terms $a^{2} b$ and $b^{3}$.
$$\text{The common factor is } b.$$

STEP 4

Factor out the common term $b$ from the expression.
$$a^{2} b - b^{3} = b(a^{2} - b^{2})$$
### Problem 19: $-98 + 2 x^{2}$
STEP_1: Simplify the expression $-98 + 2 x^{2}$ to see if further factoring or simplification is possible.
$$\text{The expression is already simplified in its current form.}$$
STEP_2: Consider if solving for $x$ is required. Set the expression equal to zero and solve for $x$ if necessary.
$$-98 + 2 x^{2} = 0$$

STEP 5

Rearrange the equation to isolate $x^{2}$.
$$2 x^{2} = 98$$

STEP 6

Solve for $x$ by dividing both sides by 2 and then taking the square root.
$$x^{2} = 49$$ $$x = \pm \sqrt{49}$$ $$x = \pm 7$$
### Solutions:
Problem 18:
$$a^{2} b - b^{3} = b(a^{2} - b^{2})$$
Problem 19:
$$x = \pm 7$$