🧮 algebra

1. সমস্যাটি হলো: উৎপাদক বিশ্বিশ্লেষণ করতে হবে \((a-1)x^2 + a^2 xy + (a+1)y^2\) এর। 2. প্রথমে আমরা ধরি এটি একটি দ্বিঘাত বহুপদী যা \(x\) এবং \(y\) এর ফর্মে লেখা আছে।

1. The problem is to analyze the quadratic form $ (a-1)x^2 + a^2 xy + (a+1)y^2 $. 2. We can write it as a quadratic form matrix: $$ Q = \begin{bmatrix} a-1 & \frac{a^2}{2} \\ \frac

1. **State the problem:** A cycle dealer marks a cycle at 20% more than the cost price and then allows a discount of 10% on the marked price. We need to find the gain percent.

1. **State the problem:** We need to find the discount percentage given the marked price (MP) and the selling price (SP). 2. **Identify the given values:**

1. **State the problem:** We need to find the discount percentage given the marked price (MP) and the selling price (SP). 2. **Identify the given values:**

1. The problem is to find the discount in percent given the original price and the discounted price. 2. The formula to calculate the discount percentage is:

1. The problem states that the marked price (m.p) is 1550 and the discount given is 8%.\n\n2. We need to find the discount amount and the selling price after applying the discount.

1. **State the problem:** Find the domain of the function $$f(x) = \frac{x}{\sqrt{3x - x}}$$. 2. **Simplify the expression inside the square root:**

1. **State the problem:** An athlete runs the same distance $x$ km on the first and second days. 2. On the third day, he runs 4 times the distance of the first day, which is $4x$ k

1. The problem is to find the value of $\frac{8}{100}$ of 1550. 2. "Of" means multiplication, so we calculate $\frac{8}{100} \times 1550$.

1. **State the problem:** Gab walks 80 steps in 2 minutes, each step is 5 dm. We need to find how many minutes it will take her to walk 5000 dm. 2. **Calculate the distance Gab wal

1. The problem states that the marked price (m.p) of an item is 1550 and the discount given is 8%.\n\n2. We need to find the selling price after applying the discount.\n\n3. The di

1. **State the problem:** Simplify the expression $a - 2b + a - b$. 2. **Group like terms:** Combine the terms with $a$ and the terms with $b$ separately.

1. **State the problem:** Simplify the expression $2x + y + 3x + 2y$. 2. **Group like terms:** Combine the terms with $x$ and the terms with $y$ separately.

1. The problem is to fully simplify the expression $5a^3 f^4 \times 3a^2 f^3$. 2. Start by multiplying the coefficients (numbers) together: $5 \times 3 = 15$.

1. **State the problem:** Simplify the expression $$6y^2 + y \times 5 + 8y \times y + 4 \times y$$. 2. **Rewrite the terms:**

1. **State the problem:** Simplify the expression $3y + 5 - y - 2$. 2. **Combine like terms:** Group the terms with $y$ and the constant terms separately.

1. **State the problem:** Expand and fully simplify the expression $$t(9t + 5) - t(t + 2)$$. 2. **Expand each term:**

1. We are given the equation $$(x^3)^8 = (x^6)^d$$ and need to find the value of $d$. 2. Apply the power of a power rule, which states $$(a^m)^n = a^{m \times n}$$.

1. **State the problem:** Simplify the expression $2x - 4 + x + 2$. 2. **Combine like terms:** Group the terms with $x$ and the constant terms separately.

1. The problem asks to express the quadratic expression $x^2 + 6x$ in the form $(x + a)^2 + b$, where $a$ and $b$ are integers. 2. Start by recalling the expansion of a perfect squ