🧮 algebra

1. **Problem statement:** (a) Factorize completely $12ab^2 + 18a^2b - 6b$

1. **State the problem:** Simplify the expression $2x(-12)$. 2. **Recall the multiplication rule:** When multiplying a variable by a number, multiply the coefficients and keep the

1. **State the problem:** Simplify the expression $3 - (-6) + 4$. 2. **Recall the rule:** Subtracting a negative number is the same as adding its positive counterpart. So, $a - (-b

1. The problem is to factor the quadratic expression $g^2 + 14g + 24$. 2. The general form of a quadratic expression is $ax^2 + bx + c$. Here, $a=1$, $b=14$, and $c=24$.

1. The problem is to graph the functions $y=5$ and $y=1.06^t$. 2. The function $y=5$ is a horizontal line where the value of $y$ is always 5 regardless of $t$.

1. The problem states that $y$ is inversely proportional to $x$, and we know $y=3$ when $x=15$. We need to find a formula for $y$ in terms of $x$. 2. When a variable $y$ is inverse

1. **State the problem:** Solve the equation $$-3 = -3| -9 - x |$$. 2. **Isolate the absolute value:** Divide both sides by $$-3$$ to simplify.

1. **Stating the problem:** Solve the system of equations using substitution or elimination method: $$\begin{cases} 8x = 5y + 2 \\ 5 - 3x = -4y \end{cases}$$

1. **Problem:** You and your business partner provided parts of the total capital needed to start a business, and the rest came from a bank loan. Find the amount from the loan. 2.

1. **State the problem:** Find the equation of the line given the x-intercept $a = -1$ and y-intercept $b = -3$. 2. **Formula:** The intercept form of the line equation is

1. **State the problem:** Solve the equation $5b = -3 + 24$ for $b$. 2. **Simplify the right side:**

1. The problem asks to find the square root of 289. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$.

1. **State the problem:** Solve the equation $$|3x| = 3$$. 2. **Recall the definition of absolute value:** For any real number $a$, $$|a| = b$$ means $$a = b$$ or $$a = -b$$, where

1. **Problem statement:** Solve the system where $\frac{x}{3} = \frac{y}{4}$ and $x^2 + y^2 = 100$. 2. **Set a common ratio:** Let $\frac{x}{3} = \frac{y}{4} = k$.

1. **Stating the problem:** We need to find the point of intersection for a system of equations. The point of intersection is where the graphs of the equations meet, meaning the va

1. **State the problem:** Find the points of intersection for each system of linear equations given. 2. **Recall the method:** The point of intersection of two lines $y=m_1x+b_1$ a

1. **Statement of the problem:** Calculate the value of $$\sqrt{7} \times (-\sqrt{7})$$ and compare it to $$ (\sqrt{7})^{100} \times (-\sqrt{7})^{100}$$.

1. The problem is to evaluate $(-5)^2$. 2. The formula for squaring a number is $a^2 = a \times a$.

1. **Problem Statement:** Mercedes multiplied $4x^3$ by the polynomial $(x^3 + 2x^2 - 3)$ and got $4x^9 + 8x^6 - 12x^3$. We need to find her error. 2. **Formula and Rules:** When m

1. **State the problem:** Evaluate the expression $-5^2$. 2. **Understand the order of operations:** According to the order of operations (PEMDAS/BODMAS), exponents are evaluated b

1. The problem asks to sort the cards into groups of equivalent expressions. 2. Let's analyze each card's expression and simplify or rewrite them to identify equivalences.