🧮 algebra

1. **Stating the problem:** Simplify or express the given expression $x^{-3} y^{4}$. 2. **Recall the rules:**

1. **Problem 1: Add the polynomials** $(3x^2 - 5y^2 + xy) + (8y^2 - 4xy - 7x^2)$. 2. **Step 1: Write the expression**:

1. **State the problem:** Evaluate the expression $$\frac{x^{-2}}{y} = \left(\frac{x}{y}\right)^2$$ when $$x=3$$ and $$y=-4$$. 2. **Recall the rules:**

1. **State the problem:** Add the polynomials $ (3x^2 - 5y^2 + 2y) + (8y^2 - 4y - 7x^2) $. 2. **Write the expression:**

1. **State the problem:** Evaluate the expression $$\frac{2x^2}{y^{-1}}$$ when $$x=3$$ and $$y=-4$$. 2. **Recall the formula and rules:** The expression is a fraction with numerato

1. **State the problem:** Given that $a - b = b - c = 2$, find the value of $$\frac{(a - b)^2 + (b - c)^2}{(a - c)^2}$$. 2. **Use the given information:** We know that $a - b = 2$

1. **State the problem:** Solve the linear equation $7x - 15 = -3x + 5$ for $x$. 2. **Write down the formula and rules:** To solve for $x$, we want to isolate $x$ on one side of th

1. **Problem a:** Simplify $$\left(\frac{4^{3}}{4^{-4}}\right)^{2 \cdot \frac{1}{2}}$$. 2. Use the property of exponents for division: $$\frac{a^{m}}{a^{n}} = a^{m-n}$$.

1. **State the problem:** We want to find and simplify $a(x-2)$ where $a(x) = 4x^{2} + 2x - 5$. 2. **Recall the function substitution:**

1. **State the problem:** We are given three functions: - $a(x) = 4x^{2} + 2x - 5$

1. The problem is to find the value of the piecewise function $$f(x) = \begin{cases} 2x+5 & \text{if } x \leq -3 \\ |x| & \text{if } x > -3 \end{cases}$$ at $$x = -1.5$$. 2. Since

1. The problem is to find the value of the function $f(x)$ at $x = -1.5$. 2. To solve this, we need the explicit formula for $f(x)$, which you have not provided. Please provide the

1. **State the problem:** We are given a piecewise function $$f(x) = \begin{cases} 2x+5 & \text{if } x \leq -3 \\ |x| & \text{if } x > -3 \end{cases}$$ and we need to find the valu

1. **State the problem:** We need to find the value of the function $b(x) = \sqrt[3]{2x - 1}$ at $x = \frac{9}{2}$. 2. **Recall the formula:** The cube root function is defined as

1. The problem asks to find the value of the function $a(x) = 4x^2 + 2x - 5$ at $x = -2$. 2. To solve this, substitute $x = -2$ into the function:

1. State the problem: The binary operation $*$ is defined on the set $\mathbb{R}$ by $a * b = \frac{ab}{4}$ and we are to find $\sqrt{2} * \sqrt{6}$.\n2. Formula and rules: Use the

1. Stating the problem: A binary operation $*$ is defined on the set $\mathbb{R}$ of real numbers by $a * b = \frac{ab}{4}$. Find $\sqrt{2} * \sqrt{6}$.\n2. Formula and rules: Use

1. **State the problem:** Simplify the algebraic expression $4d + 4a - 3a - 2c$. 2. **Group like terms:** Combine terms with the same variables.

1. **State the problem:** Simplify the expression $11x + 7 + 5 : 6 - 7x + 20x$. 2. **Clarify the expression:** The colon $:$ is often used to denote division. So the expression is

1. **State the problem:** Simplify the expression $6m - 6 + 8m$. 2. **Identify like terms:** The terms $6m$ and $8m$ are like terms because they both contain the variable $m$.

1. **State the problem:** Solve the system of equations to find the value of $y$: $$4x + 19y = 25$$