🧮 algebra

1. Problem: Simplify the expression $\left(a-b\right)^2\left(a^2 + 4\right) + \left(a-b\right)\left(a^2 + b^2\right)$. 2. Formula and rules: Use distributive property and factor co

1. **State the problem:** Solve the equation $$\frac{x-3}{2} + \frac{x+2}{3} = 5$$. 2. **Formula and rules:** To solve equations with fractions, find a common denominator to combin

1. **State the problem:** Solve the equation $$\frac{x-3}{2} + \frac{x+1}{3} = 5$$. 2. **Formula and rules:** To solve equations with fractions, find a common denominator to combin

1. Problem: Rozpisz wielomian na czynniki. 2. Załóżmy, że mamy wielomian $P(x)$, który chcemy rozłożyć na czynniki. Najczęściej stosowaną metodą jest wyciągnięcie wspólnego czynnik

1. **State the problem:** We are given the function $w(x) = -12x^{5} + 12x^{3} - 3x$ and we want to analyze or simplify it as needed. 2. **Identify the type of function:** This is

1. **State the problem:** Simplify the polynomial expression given by combining like terms: $$8mr^5 - 2rn^6 + 5mr^2n^4 - mr^3n^3 + n^6 - 4m^6 + 9rn^2n^4 - mn^5 - 4m^3rn^3$$

1. **State the problem:** We are given the polynomial $$xy^2 - 2x^2y + 3y^3 - 6x^2y + 4xy^2$$ and told that Alina wrote the last term as $$3y^3$$. We need to find the first term of

1. The problem asks to convert 125 centimeters to 87.5 centimeters and 132 days to 125.4 days, which seems to imply finding the ratio or comparison between these quantities. 2. To

1. **State the problem:** We need to find the percent change when the area increases from 100 acres to 140 acres. 2. **Formula for percent change:**

1. **State the problem:** Calculate the gross pay for the week given hourly wage, hours worked, and tips. 2. **Formula:** Gross pay = (Hourly wage × Hours worked) + (Percentage of

1. **State the problem:** Calculate the gross pay for the week given the hourly wage and work hours. 2. **Identify the hourly wage:** $14$ per hour.

1. **State the problem:** Simplify the expression $$\frac{4}{3} m^3 - \left(\frac{1}{2} m\right)^2 + \left(\frac{3}{5} mn\right)^2 - \left(\frac{1}{4} n^3\right) \left(\frac{2}{3}

1. El problema es dividir el polinomio $$3a^5 - 27a^4b + 1006 + 64a^7b^3 + 32ab^4$$ entre el polinomio $$a^2 - 5ab - 4ab^2$$. 2. Para dividir polinomios, usamos la división larga o

1. **State the problem:** James bought 15 shirts, each costing 160. He spent a total amount of money that could also buy 20 identical backpacks. We need to find the cost of one bac

1. Problema: Factorizar el área de una hilera de columnas dada por la expresión $12x^2 + 8x$. 2. Fórmula y regla: Para factorizar expresiones polinómicas, buscamos el máximo común

1. **State the problem:** We have a function $g(x) = 2x - 5$ and need to find its inverse function $g^{-1}(x)$. 2. **Find the inverse function:** To find $g^{-1}(x)$, start by sett

1. **State the problem:** We have a number $n$ with prime factorization $$n = 2^5 \times x \times y^4,$$ where $x$ and $y$ are distinct primes greater than 2. 2. **Recall the rule

1. **State the problem:** Calculate the value of $25 \times \sqrt{1127}$.\n\n2. **Formula and rules:** The square root function $\sqrt{x}$ gives the number which, when multiplied b

1. **State the problem:** Simplify the expression $25\sqrt{1127}$. 2. **Recall the formula and rules:** The square root of a product can be written as the product of square roots:

1. **State the problem:** We need to rewrite the expression $$-10m - (-7.6m + 1)$$ by distributing the minus sign outside the parentheses. 2. **Recall the rule:** When subtracting

1. **State the problem:** Simplify the expression $-(-5.8 d - 3 f - 4)$. 2. **Recall the rule:** The negative sign outside the parentheses means we multiply each term inside by $-1