🧮 algebra

1. Let's solve a new algebra problem step-by-step. 2. Consider the quadratic equation $$2x^2 - 4x - 6 = 0$$.

1. Let's first understand the structure of your question request. 2. If you want to attempt a problem similar to one you've seen before, I will create a sample question involving a

1. The problem is to express the expression $$49x^{3/2}$$ in indices (exponential) form. 2. We note that $$49$$ is a perfect square and can be written as $$7^2$$.

1. **State the problem:** Simplify the expression $5b + 6n - 2t + 3 + 3b - 4n - 5t$. 2. **Group like terms:** Group terms with $b$, $n$, $t$ and constant terms separately.

1. **Problem statement:** Fully simplify the expressions given. 2. **Part a) Simplify** $5f \times 7$.

1. The given expression is $49x^{3/2}$. 2. We want to simplify or understand this expression better.

1. State the problem: Factorize the expression $16ab^3 - 8ab + 32a^2bc^2$. 2. Identify the common factors of all terms: Each term contains at least $8ab$.

1. **State the problem:** Solve the equation $$7b + 6 = -29$$ for the variable $b$. 2. **Isolate the term with $b$:*** Subtract 6 from both sides to undo the addition.

1. The problem is to calculate the fifth root of 8, written as $\sqrt[5]{8}$. 2. Recall that the fifth root of a number $x$ is the number $y$ such that $y^5 = x$.

1. The expression given is 1+*+5+21+52+65+1. 2. We notice there is a syntax error due to the operator combination '+*+'.

1. The problem asks to simplify the expression $(2a)^{-1} \times 3a^2$. 2. First, recall that $(2a)^{-1}$ means the reciprocal of $2a$, which is $\frac{1}{2a}$.

1. The problem asks to find the cube root of 32. 2. Recall that the cube root of a number $a$ is a number $x$ such that $x^3 = a$.

1. **Problem: Expand and simplify $ (1 - x + x^2)^3 $.** 2. To expand this cube, we use the binomial expansion for a trinomial power. We write:

1. The problem is to evaluate $\sqrt[4]{9}$, which means finding the fourth root of 9. 2. Recall that the fourth root of a number $a$ is the number $x$ such that $x^4 = a$.

1. The statement claims that if $n$ is a prime number, then $2n + 1$ is also a prime number. 2. To test this, choose an example where $n$ is prime. Let's take $n = 3$, which is a p

1. The problem asks us to show that the difference between $3^2$ and $3^3$ is 18. 2. Calculate $3^2$:

1. **Problem 1:** Fajuyi borrows ₦1,000.00 at an interest rate of ₦10.00 per week and needs to repay after 4 weeks. 2. We calculate the total interest first:

1. The problem involves a girl who buys and sells bread, gaining 20 Rs on each piece sold. 2. We are given that $P = 6000$ in the user's statement, but then it also says $P = 70$ a

1. The problem asks to find the sum of the arithmetic progression (AP) series starting from 80, increasing by 1, up to 140. 2. Identify the first term $a_1 = 80$ and the last term

1. **State the problem:** Factor the polynomial $$18y^2 + py - 5$$. 2. **Identify coefficients:** The polynomial is quadratic in $y$, with coefficients: $$a = 18, b = p, c = -5$$.

1. Multiply out each given expression: a. Expand $(2x^2 + 4x - 3)(x^2 + 4x - 2)$ by distributing each term: