🧮 algebra

1. **Stating the problem:** Simplify the expression $$Fy = -10 - 9 \times 10^{-9} \cdot r \cdot \frac{3 \cdot r_0 y}{4 \pi \cdot 10^{-9} \times 10^{-4}} \div (36 \pi)$$. 2. **Rewri

1. The problem asks to use the "Sam formula" as referenced in a previous photo, but since the photo is not provided, I will explain a common algebraic formula often called "Sam's f

1. The problem is to expand and simplify the expression $(x - y)^2$ using the formula $$(a - b)^2 = a^2 - 2ab + b^2$$ 2. Applying the formula, let $a = x$ and $b = y$:

1. **State the problem:** Multiply the binomials $(x + 2)(3x + 3)$ using the area model. 2. **Formula and rules:** To multiply two binomials, use the distributive property (FOIL me

1. The problem is to simplify or understand the expression $R = Z(\sqrt{y^2 + x^2})$. 2. This expression involves the square root of the sum of squares of $x$ and $y$, which is the

1. Planteamos el problema: Determinar el dominio máximo de la función $$f(x) = \frac{\sqrt{x^3 + 4x^2 - 17x - 60}}{2x^3 + 3x^2 - 18x + 8}$$. 2. Para que la función esté definida, e

1. **State the problem:** We need to find the perimeter of a right triangle with sides labeled as $12 - 4x$, $7x + 1$, and $x - 3$. 2. **Recall the perimeter formula:** The perimet

1. **State the problem:** Simplify the expression $$(2x^2 - 7x + 1) - (-5x^2 + x - 9)$$. 2. **Formula and rules:** When subtracting polynomials, distribute the minus sign to each t

1. **State the problem:** Solve the quadratic equation $x^2 - 109 = -8x$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation equal to zero:

1. **State the problem:** Simplify the expression $$\frac{2^4 - (2^5)^8 - 2^6}{(2^4)^{33} - 16 - (2^7)^3 - 2^{10}}$$. 2. **Apply exponent rules:** Recall that $(a^m)^n = a^{m \time

1. **State the problem:** Solve the quadratic equation $$3x^2 + 228 = 54x$$ for $x$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero:

1. **State the problem:** Simplify the expression $$\frac{2^{3}-\left(2^{5}\right)^{8}-2^{6}}{\left(2^{4}\right)^{3}-16-\left(2^{7}\right)^{3}-2^{10}}$$. 2. **Recall exponent rules

1. The problem is to simplify the expression $$\frac{2^4 - (2^5)^8 - 2^6}{dx}$$. 2. First, note that the expression is written as a fraction with denominator $dx$, which suggests d

1. **State the problem:** Solve the quadratic equation $$m^2 + 2m - 3 = 0$$ using the quadratic formula. 2. **Recall the quadratic formula:** For an equation $$ax^2 + bx + c = 0$$,

1. **Problem 10:** Simplify \( \frac{a^3b^3}{xy^4} \div \frac{a^2b}{x^2y} \). 2. Division of fractions means multiplying by the reciprocal:

1. The problem is to simplify the expression $10 - \frac{}{ }$, which is incomplete as the numerator and denominator of the fraction are missing. 2. To simplify an expression invol

1. Two numbers whose sum is zero - This describes **Additive Inverse** because additive inverses are pairs of numbers that add up to zero.

1. **State the problem:** Solve the equation for $t$ given by $$10 - 3t = 3t + 2.$$ 2. **Write the formula and rules:** To solve for $t$, we want to isolate $t$ on one side of the

1. The problem is to match each description with the correct mathematical term from the given list. 2. We analyze each description and find the corresponding term:

1. **State the problem:** Simplify the expanded form of $(x - 4y)^5$. 2. **Recall the expanded form:**

1. **State the problem:** Expand and simplify the expression $$(x - 4y)^5$$ using the binomial theorem. 2. **Formula:** The binomial theorem states: