🧮 algebra

1. **State the problem:** Simplify the expression $x^2 - 2x + 1$. 2. **Recall the formula:** This is a quadratic expression that can be factored using the perfect square trinomial

1. Simplify the expression $(8 - 4) \times 5 \div 2$ using the order of operations (GEMDAS). 2. Simplify the expression $(10 - 5)^2 \div 5 + 2$ using GEMDAS.

1. Bài toán: Giải phương trình bậc hai $ax^2 + bx + c = 0$. 2. Công thức nghiệm: $$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

1. **Problem statement:** b) Find the expression for $M$ such that $$M + (5x^2 - 2xy) = 6x^2 + 9xy - y^2.$$

1. The problem is to verify that the solution you provided matches the expected solution. 2. To do this, we need to compare your solution step-by-step with the standard method or f

1. The problem is to evaluate the expression: $-7 - (11)$ using the KFC (Keep, Flip, Change) method. 2. KFC stands for:

1. The problem is to understand the phrase "Like this" in a math context and provide a relevant example or explanation. 2. Since the user did not specify a particular math problem,

1. **Problem 1: Ages of Bianca and Bryan** The age of Bianca is 4 more than 3 times the age of Bryan. The sum of their ages is 32. Find their ages.

1. **Problem Statement:** Let's understand what "Systems of Linear Equations" and "Gaussian Elimination" mean in simple language.

1. **State the problem:** Solve a linear equation in one variable, for example, $3x + 5 = 11$. 2. **Formula and rules:** A linear equation in one variable has the form $ax + b = c$

1. **State the problem:** Ely's mother is currently 35 years old. Three years ago, she was 4 times as old as Ely was at that time. We need to find Ely's current age. 2. **Define va

1. The problem is to find the result of each subtraction expression involving fractions and mixed numbers. 2. We subtract fractions by finding a common denominator and then subtrac

1. The problem is to convert the equation $y - x + 2 = 0$ into slope-intercept form. 2. The slope-intercept form of a line is given by the formula:

1. Problem: Subtract the fractions and reduce to the lowest terms. 2. Formula: To subtract fractions with the same denominator, subtract the numerators and keep the denominator the

1. Problem 16 a): Given the quadratic equation $px^2 + qx + q = 0$ with roots $\alpha$ and $\beta$, prove that $\frac{\alpha}{\sqrt{\beta}} + \frac{\beta}{\sqrt{\alpha}} = \frac{\s

1. The problem shows four inequalities involving variables A, B, C, and D with given numbers: - $A \leq 16.5$

1. The problem is to add pairs of fractions and simplify the results. 2. The formula for adding fractions with the same denominator is:

1. **Énoncé du problème :** On considère la fonction $f$ définie sur $[0; +\infty[$ par

1. The problem is to find the cube of a number, which means multiplying the number by itself three times. 2. The formula for the cube of a number $x$ is:

1. **State the problem:** We want to expand and simplify the expression $$(a + b)^4$$. 2. **Formula used:** The binomial theorem states that $$(a + b)^n = \sum_{k=0}^n \binom{n}{k}

1. **State the problem:** Simplify the expression $$\cos\left(2\left(x+2p(x^2+1)\sin(2x)+p\frac{x\cos(2x)}{(x^2+1)^{3/2}}\right)\bigg/\sqrt{\left(x+2p(x^2+1)\sin(2x)+p\frac{x\cos(2