🧮 algebra

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:

1. The problem asks to find the sum of the arithmetic progression (AP) series starting from 80, 81, 82, ..., up to 139, 140 which are 100 positive integers. 2. First, let's identif

1. Stated problem: Simplify the expression $$(-d^5)^4$$. 2. Apply the power of a power rule: $$(a^m)^n = a^{m \times n}$$, so $$(-d^5)^4 = (-1)^4 \times (d^5)^4$$.

1. **State the problem:** We want to verify and complete the square for the quadratic expression $4x^2 + 14x$. 2. **Rewrite the expression:** Write $4x^2 + 14x$ as $4x^2 + 4x + 8$

1. Stating the problem: Simplify the expression $(mn^2)^4$. 2. Apply the power to each factor inside the parentheses: $(mn^2)^4 = m^4 (n^2)^4$.