🧮 algebra

1. We are asked to factorise the expression $64x^2y^2 - 36y^2z^2$ fully. 2. First, identify the common factor in both terms. Both terms contain $y^2$, so factor it out:

1. **State the problem:** We need to factorize the quadratic expression $x^2 - 2x - 35$. 2. **Identify coefficients:** The quadratic is in the form $ax^2 + bx + c$ where $a=1$, $b=

1. **State the problem:** Simplify the expression $ (3-4x)^2 $. 2. **Apply the square of a binomial formula:** Recall that $(a-b)^2 = a^2 - 2ab + b^2$.

1. State the problem: Evaluate the square root of 368 and round the answer to 3 decimal places. 2. Use a calculator to find \( \sqrt{368} \).

1. **State the problem:** Expand and simplify the expression $$(3x+1)^2 - (2x+2)^2$$. 2. **Expand each square term:**

1. Problem: Calculate the 7th root of -29 ($\sqrt[7]{-29}$) to 2 decimal places using a calculator. 2. Since the root is odd (7), the root of a negative number is also negative: $\

1. Let's analyze the first expression (a): $4a^2 + 12ab$. 2. Factor out the greatest common factor (GCF) from both terms. The GCF of $4a^2$ and $12ab$ is $4a$.

1. Planteamos el problema: tenemos el quinto término en la expansión binomial $$ (ax + by)^n $$ dado por $$ 560 x^3 y^4 $$ y queremos encontrar los valores enteros de $$a$$ y $$b$$

1. **State the problem:** We are given the equation $$xy^3 - 4x^2 = 10y^2$$ and we want to analyze or possibly solve it for one variable in terms of the other. 2. **Rewrite the equ

1. The problem is to solve the equation $$2(\frac{1}{27})^{x+1} = 7$$ for $x$. 2. Start by isolating the exponential term: divide both sides by 2.

1. We are given the problem: Solve the equations (a) $x^3 - 1 = 0$, (b) $x^4 + 1 = 0$, (c) $x^5 + 1 = 0$, (d) $x^6 - i = 0$, (e) $x^5 = 1 + i$, and then find the roots $\alpha, \al

1. **State the problem:** Find the formula for the product $ (a+b)(a-b) $. 2. **Recall the algebraic identity:** The expression $ (a+b)(a-b) $ is a difference of squares, which mea

1. The problem states: "If 25% of a number is 75, what is the number?". 2. Let the number be $x$.

1. **State the problem:** Simplify the expression $$\frac{3}{4}+\frac{2}{5}-\frac{1}{2}$$. 2. **Find a common denominator:** The denominators are 4, 5, and 2. The least common deno

1. Stating the problem: We need to find the value of $n$ in the equation $$\frac{10n}{3} - 1.5 = 14.5$$. 2. Add $1.5$ to both sides of the equation to isolate the term with $n$: $$

1. State the problem: Solve the equation $$\frac{x + 23}{4} + 25 = 36$$. 2. Subtract 25 from both sides to isolate the fraction:

1. Let's start by stating the given equation: $$e^{x^2} y = e^y = x$$ It seems there's ambiguity in the expression as written because it contains two equal signs. Assuming the inte

1. **Stating the problem:** Solve the inequality $$3^{x-2} < \frac{3}{9^{\frac{1}{x}}}$$.

1. Išspręskime lygčių sistemą: \[

1. **State the problem:** Solve the inequality $$3^{x-2} < \frac{3}{9^{1/x}}.$$\n\n2. **Rewrite the right-hand side:** Note that $$9 = 3^2,$$ so $$9^{1/x} = (3^2)^{1/x} = 3^{2/x}.$

1. **State the problem:** Solve the inequality $$3^{x-2} < \frac{3}{9^{1/x}}.$$\n\n2. **Rewrite terms with the same base:** Note that $9 = 3^2$, so rewrite \(9^{1/x}\) as \((3^2)^{