🧮 algebra

1. **State the problem:** Subtract the polynomial $(-q^2 + 4q)$ from $(-5q^2 + 6q + 7)$. 2. **Write the expression:**

1. **State the problem:** We need to subtract the polynomial $(-3m^2 + m + 2)$ from $(-5m^2 - 8)$. This means we calculate $$(-5m^2 - 8) - (-3m^2 + m + 2).$$ 2. **Use the subtracti

1. **State the problem:** Subtract the polynomial \((a - 5)\) from \((4a^3 - 3a - 8)\) and express the result in standard polynomial form. 2. **Write the expression:**

1. **State the problem:** Subtract the polynomial \((9b - 4)\) from \((5b^3 + 9b + 4)\). We want to find \((5b^3 + 9b + 4) - (9b - 4)\). 2. **Write the subtraction explicitly:**

1. **State the problem:** Simplify the expression $$(7mn - 5mp + 8np) + (-2mn - 6np)$$ by combining like terms. 2. **Identify like terms:** Like terms have the same variables with

1. **State the problem:** We need to subtract the polynomial \( (5k^2 - 3) \) from \( (-2k + 4k^2 + 6) \). 2. **Write the expression:**

1. **State the problem:** Simplify the expression $$\frac{v^2 - 3v + 2}{v^2 - 1}$$ and find its simplified form. 2. **Recall the formula and rules:** To simplify a rational express

1. **State the problem:** Find all excluded values for the expression $$\frac{x + 8}{x^2 - 3x - 18}$$ which are values of $x$ that make the denominator zero. 2. **Recall the rule:*

1. The problem is to rearrange the formula $F = ma$ to solve for $m$. 2. The formula given is $F = ma$, where $F$ is force, $m$ is mass, and $a$ is acceleration.

1. **State the problem:** Simplify the expression \(\sqrt[6]{\sqrt{15}}\). 2. **Rewrite the expression using exponents:** The square root of 15 is \(15^{\frac{1}{2}}\), so the expr

1. **State the problem:** Simplify the expression $$\frac{\sqrt{27}}{\sqrt{12}}$$. 2. **Use the property of square roots:** $$\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$$.

1. **State the problem:** Simplify the expression $\sqrt{3a} \times \sqrt{6a}$.\n\n2. **Recall the property of square roots:** The product of square roots is the square root of the

1. The problem is to simplify the expression $-27^{1/3}$. 2. The expression involves a negative sign and a cube root. The cube root of a number $a$ is written as $a^{1/3}$.

1. The problem is to simplify the expression $-25^{1/2}$. 2. The exponent $1/2$ means the square root, so $25^{1/2} = \sqrt{25}$.

1. **State the problem:** Simplify the expression $(64n^6)^{\frac{1}{3}}$. 2. **Recall the rule:** When raising a power to a fractional exponent, use the rule $a^{\frac{m}{n}} = \s

1. **State the problem:** Simplify the expression $$(64n^3)^{\frac{1}{3}}$$. 2. **Recall the rule:** When raising a power to a fractional exponent, use the rule $$a^{\frac{m}{n}} =

1. **Problem statement:** Given the function $$f_r(x) = \frac{x^2 - 4}{|x| - 1}$$ defined on its domain, determine which of the points A(0,2), B(-2,0), C(1,0), and D(0,4) belong to

1. The problem asks if the statement $-3^{-4} = \frac{1}{81}$ is true or false. 2. Recall the order of operations: exponents are evaluated before negation.

1. The problem asks if $-8^{3/4}$ equals the 4th root of $-8^3$. 2. Recall the exponent rule: $a^{m/n} = \sqrt[n]{a^m}$.

1. The problem asks whether the 5th root of 32 equals 2. 2. The 5th root of a number $a$ is a number $b$ such that $b^5 = a$.

1. **State the problem:** Determine if the equation $$\sqrt[18]{5} = \sqrt[6]{5} \times \sqrt[3]{5}$$ is true or false. 2. **Recall the rule for roots:** The $n$th root of a number