🧮 algebra

1. **State the problem:** Expand and simplify the expression $-3(x - 2)^2$. 2. **Recall the formula:** The square of a binomial $(a - b)^2$ is expanded as $$ (a - b)^2 = a^2 - 2ab

1. **State the problem:** Expand and simplify the expression \( (2x + 1)(x - 4) \). 2. **Use the distributive property (FOIL method):**

1. The problem is to solve the equation: number 1. 2. Since the problem is not fully specified, I will interpret "number 1" as solving the equation $x=1$.

1. **State the problem:** We need to sketch the graph of the relation given by the equation $$y = -(x - 2)(x + 3)$$. 2. **Understand the equation:** This is a quadratic function in

1. **State the problem:** Find the equation of the axis of symmetry for the parabola given by the relation $$y = -2(x - 4)(x - 6)$$. 2. **Recall the formula:** The axis of symmetry

1. The problem asks for the coordinates of the vertex of the parabola given by the relation $$y = 3(x - 5)(x + 7)$$. 2. The formula for the vertex of a parabola in factored form $$

1. **State the problem:** Solve the system of linear equations: $$y = 5x + 37$$

1. The problem is to solve the system of equations: $$5x + 7y = 8$$

1. The problem is to solve the system of equations: $$2y = 7x - 9$$

1. **State the problem:** Solve the system of equations using substitution method: $$x - 3y = 12.5$$

1. **State the problem:** We are given the system of linear equations: $$2x + 3y = 5$$

1. The problem states that Trevor is solving a system of equations by elimination and after adding the equations, both variables cancel out, leaving the statement $0=0$. 2. When so

1. **State the problem:** Olivia is solving the system of equations: $$6x - 2y = -4$$

1. **Stating the problem:** We are given two inequalities involving variables and the variable $x$:

1. **Problem statement:** Calculate the value of the expression $$P = \frac{1^4 + \frac{1}{4}}{2^4 + \frac{1}{4}} \cdot \frac{3^4 + \frac{1}{4}}{4^4 + \frac{1}{4}} \cdots \frac{9^4

1. **State the problem:** Solve the linear equation $4x - 7 = 7x + 5$ for $x$. 2. **Write the formula and rules:** To solve for $x$, we want to isolate $x$ on one side. We do this

1. **State the problem:** We want to find a factor of the polynomial $$60x^4 + 56x^2 + 12$$ of the form $$ax^2 + b$$ where $$a$$ and $$b$$ are positive constants. Then, we need to

1. **State the problem:** Mai earns a fixed wage plus extra money for every hour of overtime she works. The graph shows her total pay (in dollars) versus the amount of overtime (in

1. The problem describes Deshaun walking to school at a constant rate, stopping midway, then continuing at a slower rate. 2. We need to choose the graph that best represents distan

1. The first problem is to simplify or factor the expression $x^2 + 6x + 8$. 2. We use the factoring formula for quadratic expressions: $$ax^2 + bx + c = (x + m)(x + n)$$ where $m$

1. **Problem statement:** Apply the distributive property to each expression to write an equivalent expression. 2. **Recall the distributive property:** For any expressions $a$, $b