🧮 algebra

1. The problem is to find the product of three identical 2x2 matrices: $$\begin{bmatrix}a & b \\ c & d\end{bmatrix} \times \begin{bmatrix}a & b \\ c & d\end{bmatrix} \times \begin{

1. **State the problem:** We are given the formula for the sum $S_n = n^2 - 41n$ and need to show that $S_n = 0$ for some value(s) of $n$. 2. **Set the sum equal to zero:** To find

1. **State the problem:** Expand the expression $$(3x + 2)(2x^2 - 5xy + 4y^2)$$. 2. **Formula used:** Use the distributive property (also called FOIL for binomials) which states th

1. **Problem:** Simplify the expression by combining like terms: $$(2x^3 - 3x^2 + 4x) + (-3x^3 + 5x^2 - 2x)$$

1. **State the problem:** We need to decompose a given rational function into partial fractions. However, the specific function to decompose was not provided. 2. **General formula

1. **Stating the problem:** We want to decompose the rational expression $$\frac{x^2 - 1}{x^3 + x + 1}$$ into partial fractions.

1. **State the problem:** Simplify the expression $$(4^7)^5$$. 2. **Recall the exponent rule:** When raising a power to another power, multiply the exponents: $$ (a^m)^n = a^{m \ti

1. **State the problem:** Simplify the expression $\frac{1}{2} \times (3x+1) \times (2x-3)$. 2. **Recall the distributive property:** To multiply expressions, multiply each term in

1. The problem is to simplify the expression $$(4^7)^5$$ and choose the correct equivalent power of 4. 2. We use the power of a power rule: $$(a^m)^n = a^{m \times n}$$.

1. The problem asks to write down the two inequalities that describe the unshaded region on the graph. 2. The graph shows two lines:

1. **State the problem:** Find the points of intersection between the parabola $$y = 4 - x^2$$ and the line $$y = -x + 2$$. 2. **Set the equations equal to find intersection points

1. প্রথমে সমস্যাটি বলি: f(x) = 3x - 4 এবং g(x) = x - 1 দেওয়া আছে। 2. প্রথম অসমীকরণ: $|2x - 5| < 3$ সমাধান করি।

1. Soal pertama meminta kita menentukan nilai $x$ pada persamaan yang belum disebutkan secara eksplisit. 2. Karena persamaan tidak diberikan, saya akan menjelaskan cara umum menyel

1. **State the problem:** We need to evaluate the expression $28 - 205 - 8a + 565 + 365 - 52 + 4(95 - 17)$. 2. **Understand the expression:** The expression contains subtraction, a

1. Stating the problem: Simplify the algebraic expression $x + 2y + 4x - 3y$. 2. Formula and rules: Combine like terms by adding or subtracting coefficients of the same variables.

1. Le problème semble concerner l'absence de parenthèses dans une expression mathématique. 2. Les parenthèses sont essentielles pour indiquer l'ordre des opérations dans une expres

1. Problem: A contractor hires 8 workers. How many workers are available? This is a straightforward statement, so the answer is simply 8 workers.

1. The problem is to simplify the expression $$\frac{2x}{3} = \frac{-1}{3}$$. 2. This is an equation where the fraction on the left side equals the fraction on the right side.

1. The problem is to find the sum of the integers from 1 to 10. 2. We use the formula for the sum of the first $n$ natural numbers: $$S = \frac{n(n+1)}{2}$$ where $n$ is the last n

1. The problem is to solve the equation $$\frac{2x}{3} = \frac{1}{3}$$ for $x$. 2. To solve for $x$, we use the property that if two fractions are equal and have the same denominat

1. **State the problem:** Expand and simplify the expression $$6y(5y + 4) - 5y(2y - 7)$$. 2. **Apply the distributive property:** Multiply each term inside the parentheses by the t