🧮 algebra

1. Тэгшитгэлийг уншиж ойлгоё: $$(x + \diamond)(\square x - 1) = 2x^2 + 5x + \triangle$$ 2. Зүүн талын үржвэрийг задлая:

1. **State the problem:** Simplify the expression $2cd - 2ce + d^2 - e^2$. 2. **Recall the formula:** The expression contains a difference of squares $d^2 - e^2$, which can be fact

1. **State the problem:** Solve the cubic equation $$b^3 + 6b^2 + 12626b - 75720 = 0$$ for $b$. 2. **Recall the approach:** For cubic equations, we can try to find rational roots u

1. Stating the problem: Solve the equation $x + 2x = 45$ for $x$. 2. Combine like terms on the left side: $x + 2x = 3x$.

1. **Problem Statement:** Calculate an estimate of the mean time taken by 100 students to solve a puzzle given the grouped frequency distribution:

1. **Problem statement:** Calculate an estimate of the mean time taken by 100 students to solve a puzzle given the grouped frequency distribution:

1. The problem is to plot the graph of the function $$y = 4x^4 + 6$$ and analyze the given points $(-1,10)$, $(1,6)$, $(1,10)$, $(2,70)$, and $(3,330)$. 2. The function is a polyno

1. The problem states that money is shared between Ali, Kat, and Lena in the ratio 5 : 3 : 4, and Lena's share is 76. 2. Let the common ratio factor be $k$. Then Ali's share is $5k

1. The problem asks to write the numbers $7.²$ and $21.2⁴$ in the form $\frac{a}{b}$ where $b \neq 0$. 2. First, interpret the notation: $7.²$ means $7.2$ (7 point 2) and $21.2⁴$ m

1. **Problem:** Find the equation of the line with slope 3 and y-intercept 9 in slope-intercept form. 2. **Formula:** The slope-intercept form of a line is given by $$y = mx + b$$

1. **State the problem:** Multiply and simplify the expression $$(6 + \sqrt{2})(7 + 8\sqrt{2})$$. 2. **Recall the distributive property (FOIL method):** To multiply two binomials,

1. **State the problem:** Multiply and simplify the expression $$(5 - 9\sqrt{3})(4 - 8\sqrt{3})$$. 2. **Formula used:** Use the distributive property (FOIL method) to multiply two

1. **Problem Statement:** Given the function $y = 4x^4 + 6$ with domain $x = \{-1,0,1,2,3\}$, we need to find the range values. 2. **Formula and Explanation:** The function is a po

1. The problem is to simplify the expression $x^{\frac{1}{3}} - 4x$. 2. Recall that $x^{\frac{1}{3}}$ means the cube root of $x$, and $4x$ means $4$ times $x$.

1. נניח שהפונקציה היא $f(x)$, אך לא סופק ביטוי מדויק לפונקציה. 2. כדי למצוא מתי הפונקציה מתקיימת, יש צורך בביטוי המתמטי של הפונקציה או תנאי מסוים (למשל, מתי הפונקציה שווה לאפס, מתי

1. **Stating the problem:** Solve the system of linear equations:

1. **State the problem:** Factorise the expression $2y + 8yz$. 2. **Identify common factors:** Look for the greatest common factor (GCF) in both terms. Here, both terms have a fact

1. **Problem:** Solve and analyze the quadratic equation $x^2 - 25 = 0$. 2. **Formula:** Quadratic equation standard form is $ax^2 + bx + c = 0$.

1. **Problem:** Solve and analyze the quadratic equation $x^2 - 25 = 0$. 2. **Formula:** Quadratic equation standard form is $ax^2 + bx + c = 0$.

1. The problem is to find the axis of symmetry of a quadratic function. 2. The general form of a quadratic function is $y = ax^2 + bx + c$.

1. **State the problem:** Solve the quadratic equation $$x^2 - 25 = 0$$ and sketch its graph. 2. **Formula and rules:** The standard form of a quadratic equation is $$ax^2 + bx + c