🧮 algebra

1. **State the problem:** Solve the system of linear equations using substitution method. 2. **General approach:** The substitution method involves solving one equation for one var

1. **State the problem:** Reduce the expression $$a^2b(a^3b - b^2a^2) + 4a^3b^2a^2 - 2aba^4b + 7ab^0a^4b^2 - 3a^3bab^2$$ to a standard polynomial. 2. **Distribute and simplify each

1. **State the problem:** Simplify the expression $a^2b(a^3b - b^2a^2) + 4a^3b^2a^2 - 2aba^4b + 7ab^0a^4b^2 - 3a^3bab^2$. 2. **Recall exponent rules:**

1. **State the problem:** We have a linear sequence where the first term $a_1 = 9$ and the common difference $d = 7$. We want to find the value of $n$ when the $n$th term $a_n = 38

1. **State the problem:** Simplify the expression $ (x - 3)(x + 1) + 2x(x^2 - 2x) $. 2. **Use the distributive property (FOIL) to expand each product:**

1. The problem is to calculate $0.3 \times \sqrt{2.75}$.\n\n2. The formula used is multiplication combined with the square root function: $a \times \sqrt{b}$.\n\n3. First, calculat

1. **State the problem:** Calculate the value of $2.3 \times 10^{-3} + 6.8 \times 10^{-4}$ and express the answer in standard form. 2. **Recall the rule:** To add numbers in scient

1. **Problem statement:** Given the relation $R = \{(x,y) \in \mathbb{R}^2 \mid y^2 = 4x - x^2\}$, find the domain and range of $R$ and determine if $R$ defines a function from $\m

1. **State the problem:** We want to find the sum of the infinite series $$\sum_{n=1}^\infty \frac{1}{2^n}$$ and verify that it equals 1. 2. **Formula used:** This is a geometric s

1. **State the problem:** Simplify the expression $$(x - 2)^2 + 3(x + 1)^3 - (x + 9)$$. 2. **Recall formulas:**

1. The problem is to solve the equation or expression given by the user. Since no specific problem was provided, I will demonstrate solving a simple algebraic equation as an exampl

1. **State the problem:** Simplify the expression $-2x - 2 - 2 - 2x - 8$. 2. **Combine like terms:** Group the terms with $x$ and the constant terms separately.

1. **State the problem:** Simplify the expression $$(x - 1) \cdot x^2 + 3 \cdot (x - 3)^2$$. 2. **Recall formulas and rules:**

1. **State the problem:** Solve the inequality $$3^8 \leq -2x^2$$ for $x$. 2. **Analyze the inequality:** The left side is $3^8$, a positive constant, and the right side is $-2x^2$

1. The problem asks to select all functions whose inverses are also functions. 2. A function has an inverse that is also a function if and only if it is one-to-one (passes the hori

1. The problem is to find the domain and range of the inverse function of $$s(x) = \frac{6x - 1}{x + 5}$$. 2. To find the inverse, swap $$x$$ and $$y$$ and solve for $$y$$:

1. **State the problem:** Write the expression $ (x - 1)^2 - x(x + 1)(x - 3) $ as a standard polynomial. 2. **Expand each part:**

1. **State the problem:** We need to find the first term $a$ and the common difference $p$ of an arithmetic progression (AP) given that the 5th term is 20 and the 10th term is 40.

1. **State the problem:** We know that in 2005, the Product Development department had 150 employees, which is 25% less than in 2000. We need to find how many employees worked in t

1. The problem is to solve the equation given by the user. However, no specific equation was provided, so I will demonstrate solving a simple algebraic equation as an example: $2x

1. **State the problem:** Express the sums using summation notation. 2. **Sum 1:** $1^3 + 2^3 + 3^3 + \dots + 9^3$