Algebra

Expand $(x - y + 1)^2$.

Find the expansion of $(a + \frac{2}{a})^2$.

What is the expansion of $(x + 9)^2$?

Expand $(11a + 1)^2$.

Find the value of $101^3$ using the identity $(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$.

If $x - \frac{1}{x} = 3$, find the value of $x^4 + \frac{1}{x^4}$.

Simplify $(x - y + z)^2 - (x + y - z)^2$.

If $a+b=1$ and $a^2+b^2=2$, find the value of $a^3+b^3$.

If $x + \frac{1}{x} = p$, find the value of $x^5 + \frac{1}{x^5}$.

If $a=x-y$, $b=y-z$, and $c=z-x$, find the value of $a^3+b^3+c^3$.

Factorize by common binomial: $a(b - c) - d(b - c)$

Factorize the trinomial: $x^2 + 12x + 35$

Factorize: $y^2 - 18y + 81$

Factorize the expression: $m^2 - 144$

Factorize the expression: $4x^2 - 9y^2 - 2x - 3y$

Factorize: $x^2 - y^2 + 6y - 9$

Factorize: $a^3 - 8b^3$

Factorize $x^3 - 23x^2 + 142x - 120$ into three linear factors.

Factorize $x^2 + \frac{1}{x^2} - 3$.

Factorize $a^4 + 4b^4$.

The sum of two numbers is 18 and one number is twice the other. What are the numbers?

In the system $5x + 2y = 16$, if $y = 3$, find the value of $x$.

Express $x$ in terms of $y$ using the equation $x - 2y = 5$.

Solve the system: $x + y = 6$ and $x - y = -2$.

Solve for $x$ and $y$: $\frac{x}{3} + \frac{y}{2} = 3$ and $x - 2y = 2$.

Solve the system: $12x + 13y = 25$ and $13x + 12y = 25$.

Solve for $x$ and $y$: $x - y = 0.9$ and $\frac{11}{2(x+y)} = 1$.

Solve for $x$ and $y$: $\frac{ax}{b} - \frac{by}{a} = a+b$ and $ax - by = 2ab$.

The sum of a two-digit number and the number obtained by reversing the order of its digits is 121. If the digits differ by 3, find the number.

Solve the equations: $\frac{2}{x} + \frac{3}{y} = \frac{9}{xy}$ and $\frac{4}{x} + \frac{9}{y} = \frac{21}{xy}$.

Evaluate $2^3 + 2^2 + 2^1$.

If $10^x = 0.1$, find $x$.

Find the value of $(\frac{27}{64})^{\frac{1}{3}}$.

Evaluate $81^{0.5}$.

Evaluate the value of $\frac{2^n + 2^{n-1}}{2^{n+1} - 2^n}$.

If $a = x^l y^{m+n}$, $b = x^m y^{n+l}$ and $c = x^n y^{l+m}$, find the value of $a^{m-n} b^{n-l} c^{l-m}$.

Solve for $x$: $2^{2x+3} - 9 \cdot 2^x + 1 = 0$.

If $10^{x} = 64$, what is the value of $10^{\frac{x}{2} + 1}$?

Find $x$ if $5^{x-3} \cdot 3^{2x-8} = 225$.

Solve for $x$: $x^{x\sqrt{x}} = (x\sqrt{x})^x$

What is the value of $\log_2 1$?

Calculate the value of $\log 10 + \log 100$.

Evaluate $\log_{25} 5$.

What is the value of $\log_a \left(\frac{1}{a}\right)$?

Solve for $x$: $\log_{2} x + \log_{4} x = 3$.

If $\log_{10} x = a$, express $10^{a-2}$ in terms of $x$.

Find the value of $\log_2 (0.25)$.

If $a = \log_{24} 12, b = \log_{36} 24, c = \log_{48} 36$, find $1+abc$.

Solve for $x$: $\log_{x} (3x^2 + 10x) = 3$.

If $\log_a x = p$ and $\log_b x = q$, find $\log_{ab} x$.