Identify the rule of algebra being demonstrated.

$$(10 x) y-10(x y)$$

use the algebraic tests to check for symmetry with respect to both axes and the origin. x - y^2 = 0

Solve the quadratic equation by factoring. $2 x^{2}=19 x+33$

Determine whether the equation is an identity or a conditional equation.

$$3(x+2)-5=3 x+1$$

write the complex number in standard form. -4i^2 + 2i

Write an algebraic expression for the verbal description. The sum of the squares of two consecutive even integers, the first of which is $2 n$

Find the real solution(s) of the polynomial equation. Check your solution(s). $x^{4}+5 x^{2}-36=0$

Determine whether the value of $x$ is a solution of the inequality.

Inequality: $5 x-12>0$

Values: $x=\frac{3}{2}$

Determine whether the value of $x$ is a solution of the inequality.

Inequality: $5 x-12>0$

Values: $x=\frac{5}{2}$

Determine whether the value of $x$ is a solution of the inequality.

Inequality: $5 x-12>0$

Values: $x=-3$

Determine whether the value of $x$ is a solution of the inequality.

Inequality: $5 x-12>0$

Values: $x=3$

Write a quadratic equation that has the given solutions. (There are many correct answers.)

$-3$ and $6$

Solve the equations, given that $a$ and $b$ are not zero.

$$a x^2-a x=0$$

Solve the equations, given that $a$ and $b$ are not zero.

$$a x^2+b x=0$$