🧮 algebra

1. **State the problem:** Simplify the expression $ax^{3} + ax^{2}$ without factoring. 2. **Recall the expression:** The given expression is $ax^{3} + ax^{2}$.

1. **State the problem:** Simplify the expression $ax^3 + ax^2$. 2. **Formula and rules:** To simplify expressions like this, we use the distributive property: $a(b + c) = ab + ac$

1. **State the problem:** Factorise the expression $ab^2 + a^2b$. 2. **Identify common factors:** Both terms contain the variables $a$ and $b$.

1. **State the problem:** We need to simplify the expression $\frac{m-7}{3}$. 2. **Formula and rules:** Division of an expression by a number means dividing each term in the numera

1. **Problem statement:** Expand $$\sqrt{\frac{1+m}{1-m}}$$ in ascending powers of $m$ up to and including the term in $m^3$. State the values of $m$ for which the expansion is val

1. **State the problem:** We need to find which equation matches the line passing through points $(-8, -8)$ and $(8, 4)$.\n\n2. **Find the slope of the line:** The slope formula is

1. **Stating the problem:** We need to find the value of the expression $\frac{6!}{3!} + 4$. 2. **Recall the factorial definition:**

1. Masalah yang diberikan adalah menentukan nilai dari ekspresi $\frac{6!}{3!} + 4$. 2. Faktorial ($n!$) adalah hasil perkalian semua bilangan bulat positif dari 1 sampai $n$. Cont

1. **State the problem:** We have an element with an initial mass of 420 grams that decays by 11.8% per minute. We want to find how much of the element remains after 16 minutes, ro

1. **State the problem:** We have an element with an initial mass of 420 grams that decays by 11.8% per minute. We want to find how much of the element remains after 16 minutes, ro

1. **Problem Statement:** Set a sample algebra question: Solve for $x$ in the equation $$2x + 3 = 11$$.

1. **State the problem:** We are given the equation $$\sqrt{\frac{2x + 3}{2}} = y + 1$$ and need to express $x$ in terms of $y$. 2. **Isolate and square both sides:** To eliminate

1. Problema: Resolver a equação $2x + 3 = 7$. 2. Isolar o termo com $x$: $2x = 7 - 3$

1. **State the problem:** Given the equation $$\frac{3x + 3x + 3x}{4} = 7$$, find the value of $$18x - 6$$.

1. **State the problem:** Simplify the expression $$(2x + 1)(x - 2) - 3(x - 2)$$ and find which option it is equivalent to. 2. **Use the distributive property:** Expand each term.

1. Diberikan ekspresi: $$\frac{30x^3 y^{-2}}{\sqrt{25x^{-2} y^8}} \times (y^{24})^{\frac{1}{2}}$$ 2. Kita mulai dengan menyederhanakan bagian penyebut: $$\sqrt{25x^{-2} y^8} = \sqr

1. We are asked to solve the quadratic equation $x^2 + 6x + 20 = 0$. 2. The general form of a quadratic equation is $ax^2 + bx + c = 0$. Here, $a=1$, $b=6$, and $c=20$.

1. The problem is to factorize the expression $$y^2 - \frac{1}{9}$$. 2. This is a difference of squares, which follows the formula $$a^2 - b^2 = (a - b)(a + b)$$.

1. **State the problem:** Factorize completely the expression $$x^4 - x^2$$. 2. **Identify the common factor:** Notice that both terms have a common factor of $$x^2$$. So, we can f

1. The problem is to factorize the expression $$25x^2 - 36y^2$$. 2. This is a difference of squares, which follows the formula $$a^2 - b^2 = (a + b)(a - b)$$.

1. **Problem Statement:** Factorize the expression $x^2 y^2 - 4$. 2. **Formula Used:** Recognize this as a difference of squares, which follows the rule: