Question

Help its due today!!

1. What is the product of 1/2-1/4? Write your answer in standard form.

A) Show your work.

B) Is the product of 1/2x-1/4 and 5x^2-2x+6 equal to product of 1/4x-1/2 and 5x^2-2x+6?Explain your answer.

Answer 1

Answer: No,  $Product\ of\ \frac{1}{2}x-\frac{1}{4}\ and\ 5x^2-2x+6\text{ is not equal to Product of }\frac{1}{4}x-\frac{1}{2}\ and\ 5x^2-2x+6$

Step-by-step explanation:

Since we have given that

1) Product of $\frac{1}{2}x-\frac{1}{4}\ and\ 5x^2-2x+6$

So, the product becomes,

$(\frac{1}{2}x-\frac{1}{4})(5x^2-2x+6)\\\\=\frac{x}{2}(5x^2-2x+6)-\frac{1}{4}(5x^2-2x+6)\\\\=\frac{5x^3}{2}-x^2+3x-\frac{5x^2}{4}+\frac{1x}{2}-\frac{3}{2}\\\\=\frac{5x^3}{2}-\frac{5x^2}{4}-x^2+3x+\frac{x}{2}-\frac{3}{2}\\\\=\frac{5x^3}{2}-\frac{9x^2}{4}+\frac{7x}{2}-\frac{3}{2}$

2)Product of $\frac{1}{4}x-\frac{1}{2}\ and\ 5x^2-2x+6$

is given by

$(\frac{1}{4}x-\frac{1}{2})(5x^2-2x+6)\\\\=\frac{x}{4}(5x^2-2x+6)-\frac{1}{2}(5x^2-2x+6)\\\\=\frac{5x^3}{4}-\frac{1}{2}x^2+\frac{3x}{2}-\frac{5x^2}{2}+x-3\\\\=\frac{5x^3}{4}-\frac{6x^2}{2}+\frac{5x}{2}-3\\\\=\frac{5x^3}{4}-3x^2+\frac{5x}{2}-3$

No, Product of $\frac{1}{2}x-\frac{1}{4}\ and\ 5x^2-2x+6$ is not equal to Product of $\frac{1}{4}x-\frac{1}{2}\ and\ 5x^2-2x+6$