🧮 algebra

1. **State the problem:** Expand the expression $ (x + 3)(x + 4) $. 2. **Formula used:** Use the distributive property (also known as FOIL for binomials):

1. **State the problem:** Expand the expression $-3(2x - 5)$. 2. **Formula used:** To expand an expression like $a(b + c)$, use the distributive property: $$a(b + c) = ab + ac$$

1. **State the problem:** Solve the system of equations by substitution: $$4x - 3y = 5$$

1. **State the problem:** Solve the system of equations by substitution: $$4x - 3y = 9$$

1. **State the problem:** Solve the linear equation $4x - 3y = 5$ for $y$ in terms of $x$. 2. **Formula and rules:** To solve for $y$, isolate $y$ on one side of the equation. Reme

1. Let's start by understanding the problem: you want to see the working steps for simplifying an expression or solving a problem. Since you didn't specify the exact problem, I'll

1. **Simplify the expression:** Given: $3a + 5b = 2c + 4a - 4b + 2c$

1. **State the problem:** Factorise completely the expression $$4x^3y - 2xy^2$$. 2. **Identify the common factors:** Look for the greatest common factor (GCF) in both terms.

1. The problem states values for variables: $a=\frac{1}{2}$, $b=2$, $c=3$, and $d=4$. It asks which one is correct, but no equation or condition is given to verify correctness. 2.

1. The problem involves solving or analyzing the equation given previously (not explicitly restated here). 2. Step 5 typically involves a key part of the solution such as simplific

1. Solve the system of equations using the inverse method or Cramer's Rule. **i.**

1. Let's start by understanding what it means to "factor out." Factoring out is the process of finding the greatest common factor (GCF) of terms in an expression and rewriting the

1. **Énoncé du problème :** On a les expressions suivantes :

1. **State the problem:** Simplify or analyze the cubic polynomial $2x^3 - 3x^2 - 11x + 6$. 2. **Formula and rules:** To factor a cubic polynomial, we can try to find rational root

1. **Problem Statement:** Factorize a polynomial using the Factor Theorem. 2. **Factor Theorem:** If $f(c) = 0$ for a polynomial $f(x)$, then $(x - c)$ is a factor of $f(x)$.

1. Evaluate $p^2$ with $p=2$: $$p^2 = 2^2 = 4$$

1. **State the problem:** Solve the inequality $5x^2 + x \ge 4$. 2. **Rewrite the inequality:** Move all terms to one side to set the inequality to zero:

1. **State the problem:** Solve the equation $$2(2x-1)^4 - 3(2x-1)^2 + 1 = 0$$ for $x$. 2. **Use substitution:** Let $$y = (2x-1)^2$$. Then the equation becomes $$2y^2 - 3y + 1 = 0

1. **State the problem:** We need to simplify and understand the function $y = |4 - 2|x||$. 2. **Simplify the absolute values:** First, calculate the inner absolute value $|4 - 2|$

1. **State the problem:** Solve the equation $$x^2 - 3|x-1| = 0$$ for $x$. 2. **Understand the absolute value:** Recall that $$|x-1| = \begin{cases} x-1 & \text{if } x \geq 1 \\ -(

1. **State the problem:** Solve the equation $$\sqrt{x^2 + 3} - 2x + 1 = 0$$ for $x$. 2. **Isolate the square root:** Move other terms to the right side: