Question

examples: simplify the following
$\frac{16x^{2}-12x+8}{4}$
$\frac{16x^{2}+48x+20}{8x+4}$
$4n(6n + 7)$
$(8x + 2)(x + 6)$

Explanation:

1. Simplify $\frac{16x^2 -12x +8}{4}$

Step1: Split the fraction

$\frac{16x^2}{4} - \frac{12x}{4} + \frac{8}{4}$

Step2: Divide each term

$4x^2 - 3x + 2$

2. Simplify $\frac{16x^2 +48x +20}{8x +4}$

Step1: Factor numerator and denominator

Numerator: $4(4x^2 +12x +5)=4(2x+1)(2x+5)$
Denominator: $4(2x+1)$

Step2: Cancel common factors

$\frac{4(2x+1)(2x+5)}{4(2x+1)} = 2x+5$ (where $x
eq -\frac{1}{2}$)

3. Simplify $4n(6n +7)$

Step1: Distribute the $4n$

$4n \cdot 6n + 4n \cdot 7$

Step2: Calculate each product

$24n^2 + 28n$

4. Simplify $(8x +2)(x +6)$

Step1: Apply FOIL method

$8x \cdot x + 8x \cdot 6 + 2 \cdot x + 2 \cdot 6$

Step2: Calculate and combine terms

$8x^2 + 48x + 2x + 12 = 8x^2 + 50x + 12$

Answer:

1. $4x^2 - 3x + 2$
2. $2x+5$ (with $x

eq -\frac{1}{2}$)

1. $24n^2 + 28n$
2. $8x^2 + 50x + 12$