Simplify the following expressions: 1. a3 - 3ab(a-b) - b3 2. Distance between A(3,0) and B(0,3) 3. If log10 x = 0, what is x?

This is the expansion of the binomial cube $(a-b)^3$.
$$
(a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3
$$
Therefore, the expression is equal to $(a-b)^3$.
*   **B) $(a-b)^3$**

2. Step 1: Use the distance formula between two points $(x_1, y_1)$ and $(x_2, y_2)$: $D = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}$

$$
D = \sqrt{9 \times 2}
$$
$$
D = 3\sqrt{2}
$$
The distance is $3\sqrt{2}$ units.
*   **C) $3\sqrt{2}$ units**

3. Step 1: Convert the logarithmic equation to exponential form. If $\log_{b} x = y$, then $b^y = x$.

Any non-zero number raised to the power of 0 is 1.
$$
x = 1
$$
*   **B) 1**

4. Step 1: Recognize the expression as a difference of squares. The formula is $(a+b)(a-b) = a^2 - b^2$.

$$
(4 + \sqrt{14})(4 - \sqrt{14}) = 4^2 - (\sqrt{14})^2
$$
$$
= 16 - 14
$$
$$
= 2
$$
*   **A) 2**

5. Step 1: Multiply the coefficients and the imaginary units. $(-5i)(-2i) = (-5) \times (-2) \times i \times i$ $= 10i^2$

Recall that $i^2 = -1$.
$$
= 10(-1)
$$
$$
= -10
$$
*   **A) -10**

6. The two coordinate axes, the x-axis and the y-axis, are perpendicular to each other. Perpendicular lines intersect at an angle of $90^\circ$. * B) $90^\circ$

7. Step 1: Factorize both expressions. $$x^4 - y^4 = (x^2)^2 - (y^2)^2 = (x^2 - y^2)(x^2 + y^2)$$ The second expression is $x^2 - y^2$.

$$
\text{LCM} = x^4 - y^4
$$
*   **C) $x^4 - y^4$**

8. A surd is an irrational number that can be expressed as a root of an integer. $\sqrt{5}$ is an irrational number because 5 is not a perfect square. Since it consists of a single term, it is a monomial surd. * A) Monomial surd

9. The additive identity in the set of real numbers ($\mathbb{R}$) is the number that, when added to any real number, leaves the number unchanged. This number is 0.

   • A) 0

10. In a logarithm, the mantissa is the fractional part of the logarithm. The integer part is called the characteristic.

    • B) Mantissa

11. In the Cartesian coordinate system, a point with both negative x and negative y coordinates (e.g., $(-4, -3)$) is located in the 3rd quadrant.

    • C) 3rd quadrant

12. The medians of a triangle are line segments joining a vertex to the midpoint of the opposite side. They intersect at the centroid, which divides each median in a $2:1$ ratio.

    • D) Medians

13. A horizontal line of the form $y = c$ (where $c$ is a constant, like $y=5$) is always parallel to the x-axis.

    • A) x-axis

14. A quadratic equation is a polynomial equation where the highest power of the variable is 2.

    • C) 2

15. According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

    • B) Greater