🧮 algebra

1. Problem: Simplify and evaluate the given algebraic expressions and products. 2. Use the difference of squares formula for expressions like $(a+b)(a-b) = a^2 - b^2$.

1. The problem is to analyze the equation $y = -4$. 2. This is a horizontal line where the value of $y$ is always $-4$ regardless of $x$.

1. **State the problem:** Solve the equation $$(x + 4)\sqrt{2x} - 4 = (x + 4)(x - 1)$$ for $x$. 2. **Rewrite the equation:** The equation is $$(x + 4)\sqrt{2x} - 4 = (x + 4)(x - 1)

1. Let's solve each quadratic equation step-by-step. 2. For equation a) $(x - 4) = 0$:

1. **State the problem:** Show that $(x + 4)$ is a factor of the polynomial $5x^3 - 73x + 28$. 2. **Recall the Factor Theorem:** A polynomial $f(x)$ has a factor $(x - a)$ if and o

1. **Problem Statement:** Factorize the given polynomials. 2. **Formula and Rules:**

1. **Problem statement:** (a)(i) The first term $a_1$ of an arithmetic progression (AP) is 3 and the sum of its 8 terms $S_8$ is 164. Find the common difference $d$.

1. Solve $x^3 = 8$. The cube root formula is $x = \sqrt[3]{a}$ where $a$ is the number on the right side.

1. **Problem statement:** (a) Find $r^n$.

1. We are asked to rewrite each expression without brackets or negative exponents. 2. Recall the rules:

1. The problem is unclear as no table or data is provided to identify what is missing. 2. To assist effectively, please provide the table or specify the data or values you want to

1. **State the problem:** Simplify each expression of the form $\left(\frac{a}{b}\right)^{-n}$ or mixed fraction raised to a negative power, giving answers in simplest rational for

1. Problem: Misha and Masha eat together at a restaurant. The total cost including tax is 132000. The tax is 18000, and they split the food cost equally. Find how much each pays. S

1. **State the problem:** Simplify each expression involving division of powers with the same base. 2. **Formula used:** For any base $a \neq 0$ and integers $m, n$, the rule is:

1. The problem is to find the y-coordinate of the vertex of a parabola given by a quadratic function. 2. The general form of a quadratic function is $$y = ax^2 + bx + c$$ where $a$

1. Write as a fraction: a) $a t^{-1} = \frac{a}{t}$

1. **Problem statement:** Given functions $f(x) = 3x + 2$, $g(x) = x^2 + 1$, and $h(x) = 4^x$, solve the following: (a) Find $h(3)$.

1. Simplify expressions with zero exponents: - Any nonzero number raised to the zero power equals 1: $a^0 = 1$ if $a \neq 0$.

1. **Énoncé du problème :** Développer puis réduire les expressions suivantes : - $-2a(3a-4)$

1. **State the problem:** Simplify the expression $$\frac{4R^2 - 2a^2}{\sqrt{4R^2 - a^2}}$$. 2. **Identify the components:** The numerator is $$4R^2 - 2a^2$$ and the denominator is

1. **Problem Statement:** Solve the equation $$|x - 3|^{3x^2 - 10x + 3} = 1$$ and explain why $$x = 3$$ is rejected but $$x = \frac{1}{3}$$ is accepted. 2. **Formula and Rules:** F