Algebra

Factorize $8b - 20$.

Simplify the expression $7 + 3x + 2$.

Expand $-2(4 - 3x)$.

Evaluate $x/y$ when $x = 12$ and $y = 3$.

Simplify the expression: $5x - [2x - (x - 3)]$.

Expand and simplify $(x - 2)(x^2 + 2x + 4)$.

Factorize $4x^2 - 20x + 25$ completely.

Find the value of $\frac{0.78 \times 0.78 - 0.22 \times 0.22}{0.78 - 0.22}$.

Expand $(x+2)(x-2)(x^2+4)$.

If $x-y=5$ and $xy=6$, find the value of $x^2+y^2$.

Expand the expression: $4c(c + d)$

Simplify: $z(5 - z)$

Expand: $2(w^2 + w + 3)$

Find the product: $5x(3x)$

Find the product: $(a - 0.1)(a + 0.1)$

Simplify: $(x+y)(x-y) + (y+z)(y-z) + (z+x)(z-x)$

Expand and simplify: $(3y - 1)(2y^2 + 4y - 5)$

Simplify: $(x^2 - y^2)^2 - (x^2 + y^2)^2$

Expand and simplify: $(x + a)(x + b)(x + c)$ where $a=1, b=-2, c=3$

Find the product: $(a^2 - 2ab + b^2)(a + b)$

Factorize $5p^2 - 20p$ completely.

Factorize the expression $m^2 + m - 12$.

What is the factorized form of $x^2 - 900$?

Factorize $2a^2 + 6a$ completely.

Factorize the trinomial $x^2 + 5x - 36$.

Factorize the expression $6x^2 - 3x + 8x - 4$ by grouping.

What are the factors of the trinomial $x^2 - 3x - 40$?

Factorize $a^2 - b^2 - 7a + 7b$ completely by grouping.

Completely factorize $12x^2 - 5x - 2$.

Factorize the expression $x^2 - y^2 - 10x + 25$ completely.

Determine the value of $a$ if $a + 25 = 0$.

Solve the equation: $50 = 2x + 10$.

Calculate the value of $s$ in the equation $\frac{s}{10} = 0.1$.

Solve for $y$: $3y + 6 = 18$.

Find the value of $x$ that satisfies $4x - 3(x - 2) = 12$.

Solve the equation $1.2(y - 5) = 0.6y$ for $y$.

Solve for $x$: $\frac{5x}{6} - \frac{x}{2} = 2$.

Solve for $x$: $2(x - 0.1) = 0.5(x + 0.8)$

Find $x$ in the equation: $0.04x + 0.15(100 - x) = 7$

Solve for $x$: $\frac{x-2}{3} + \frac{x-3}{4} = \frac{x-4}{5}$

What is the gradient of a line that passes through the points $(0, 5)$ and $(1, 5)$?

If you start at $(4, 4)$ and move $5$ units vertically downwards, what is the new position?

Which point in Quadrant II is exactly $3$ units from both the $x$-axis and the $y$-axis?

Which type of line has a gradient that is considered 'undefined'?

Does the line $y = 2x - 5$ pass through Quadrant II?

Calculate the gradient of the line passing through $(0.5, 1)$ and $(1, 2)$.

On the line $y = 3x - 1$, if the $y$-coordinate is $11$, what is the $x$-coordinate?

A line passes through $(1, 1)$ and is perpendicular to the line joining $(2, 5)$ and $(-2, 3)$. What is the $y$-intercept of this line?

Find the gradient of the line that passes through the origin and the point of intersection of $x + 2y = 8$ and $3x - y = 3$.

Line $L_1$ with equation $y = mx + 4$ and line $L_2$ with equation $y = 2x + c$ intersect at the point $(1, 6)$. Find the value of $m + c$.

Simplify the following expression: $\frac{20a^5}{4a^2}$

Simplify: $\frac{(x+y)^2}{x+y}$

Simplify the subtraction: $\frac{x+1}{y} - \frac{1}{y}$

Simplify: $\frac{14m}{7n}$

Simplify the fraction $\frac{14ab^2}{7a^2b}$.

Calculate the difference: $\frac{1}{x} - \frac{2}{3x}$.

Simplify the fraction $\frac{7x - 14}{x - 2}$.

If $\frac{x}{y} = \frac{2}{3}$, find the value of $\frac{3x+2y}{3x-2y}$.

Simplify $\frac{x^2 - x - 20}{x^2 - 25}$.

Simplify $\frac{2}{x} - \frac{x}{2} \div \frac{x+2}{4}$.

Solve: $3x \ge 9$ and $x + 2 \le 8$.

Which inequality represents '$x$ is at least 1 and at most 10'?

Solve for $x$: $10 < x + 10 < 20$.

Solve: $x - 7 < -10$ or $x - 7 > -4$.

If $x$ is an integer, how many solutions are there for $1 < 2x - 3 < 10$?

Solve the compound inequality: $3x + 1 < -8$ or $x - 4 > 2$.

Solve the double inequality: $-1 \le \frac{x-4}{2} \le 1$.

Which set of integers satisfies $x + 2 > 0$ and $2x - 5 \le 1$?

Solve the double inequality: $2x + 1 < 3x - 2 < 2x + 5$.

Solve the compound inequality: $3(2x - 1) > 9$ or $2(x + 3) < 0$.

Rearrange $y = \frac{x}{5} + 10$ to make $x$ the subject.

Make $x$ the subject of the formula: $y = 7x - 2$.

Rearrange $V = \frac{1}{3}Bh$ to make $B$ the subject.

Make $x$ the subject of the formula: $y = x^2$ (assume $x > 0$).

Rearrange the equation $2y - 5k = 3x + 1$ to make $k$ the subject of the formula.

The kinetic energy $K$ of a moving object is calculated using the formula $K = \frac{1}{2}mv^2$, where $m$ is the mass and $v$ is the velocity. Express $m$ in terms of $K$ and $v$.

The sum of the interior angles of a polygon with $n$ sides is given by the formula $S = 180(n - 2)$. Rearrange this formula to make $n$ the subject.

Rearrange $m = \frac{k^2 v}{g + k^2}$ to make $k$ the subject, given $k > 0$.

Make $x$ the subject of $y = \frac{x - a}{x + a}$.

Rearrange $P = \sqrt{\frac{ab}{c}}$ to make $c$ the subject.

Identify the values of $x$ that satisfy $x^2 + 5x = 0$.

Solve for $x$: $x^2 = \frac{1}{4}$.

What is the coefficient of $x^2$ in the equation $x^2 - x - 1 = 0$?

Solve the equation $x^2 - 2x - 15 = 0$.

Solve for $x$: $(x - 10)(x + 10) = -19$.