🧮 algebra

1. **Problem 1:** Simplify and factor $ (4x^2 - 16x + 7)(4x^2 - 16x + 15) + 16$. - Let $y = 4x^2 - 16x$. Rewrite expression as $(y + 7)(y + 15) + 16$

1. **Problem:** Simplify and expand the expressions given. 2. For the first expression:

1. Stating the problem: You asked to factorize an expression using factorization type IV, which typically is the method of factoring using grouping or a specific advanced technique

1. The problem is to factorize $q^3 - 4^3$. 2. Recognize that this is a difference of cubes, which has the formula $$a^3 - b^3 = (a-b)(a^2 + ab + b^2).$$

1. We start with the expression $(4x^2 - 16x + 7)(4x^2 - 16x + 15) + 16$. 2. Multiply the two quadratics:

1. **Write the polynomial in standard form.** The standard form orders terms from highest degree to lowest: $$f(x) = 3x^5 + x^3 + 2x + 4$$

1. The problem asks to write the polynomial function $$f(x) = 2x + x^3 + 3x^5 + 4$$ in standard form. Standard form means writing the terms from the highest degree to the lowest de

1. Simplify each expression step-by-step: i. Simplify \(2\sqrt{8} + \sqrt{18} - \frac{6}{\sqrt{2}}\):

1. **State the problem:** Arniel received a 15% discount on a T-shirt priced at 895. We need to find: - How much Arniel paid for the T-shirt.

1. **Arniel's T-shirt discount problem** 1. The original price of the T-shirt is ₱895 and the discount given is 15%.

1. Simplify each expression as requested: (a) Simplify $\sqrt[3]{252 x^{5}}$.

1. Stated problem: Solve the system of linear equations and analyze the graph of the two lines: $$6x - 7y = 40$$

1. Stating the problem: We need to find the markup price and the selling price per box of mango bars given the original price and the markup percentage. 2. Given data:

1. **State the problem:** Thirdy paid 15291.50 after a 15% discount on a cellphone. We need to find the original price and the amount of discount. 2. **Define variables:** Let the

1. The problem asks to express the logarithmic equation \(\log(\frac{1}{8}) = -1\) in its equivalent exponential form. 2. Recall that \(\log_b(a) = c\) is equivalent to \(b^c = a\)

1. Understanding the problem: You provided the numbers 5, 3, 15 and the number 9, and you ask for an explanation "in quantitative" form, which is likely a question about the quanti

1. The problem asks to express the equation $\frac{\log \frac{1}{8}}{\log 8} = -1$ as an equivalent exponent. 2. Recall that $\log a = b$ means $10^b = a$ if the log is base 10 (co

1. (a) The problem states two conditions for an arithmetic progression (AP): the sum of the first 6 terms $S_6 = 72$ and the 8th term $a_8 = 16$. (i) Recall the formula for the $n^

1. **Problem statement:** (i) Find the common difference $a$ given $a_{11}=7$, $a_{22}=54$, and the sum of the first 6 terms of an arithmetic progression (AP) is 72 where the 8th t

1. The user asked to see the shape of a function, without specifying any particular function. 2. I will provide a simple example of a quadratic function $y = x^2$, which is a class

1. Solve the following exponential equations: i. Solve $3^{3-x} = 27^{x-1}$.