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\ (1)/(2)x-(1)/(4)\ and\ 5x^2-2x+6\text{ is not equal to Product of }(1)/(4)x-(1)/(2)\ and\ 5x^2-2x+6`

Explanation:

Since we have given that

1) Product of
`(1)/(2)x-(1)/(4)\ and\ 5x^2-2x+6`

So, the product becomes,

`((1)/(2)x-(1)/(4))(5x^2-2x+6)\\\\=(x)/(2)(5x^2-2x+6)-(1)/(4)(5x^2-2x+6)\\\\=(5x^3)/(2)-x^2+3x-(5x^2)/(4)+(1x)/(2)-(3)/(2)\\\\=(5x^3)/(2)-(5x^2)/(4)-x^2+3x+(x)/(2)-(3)/(2)\\\\=(5x^3)/(2)-(9x^2)/(4)+(7x)/(2)-(3)/(2)`

2)Product of
`(1)/(4)x-(1)/(2)\ and\ 5x^2-2x+6`

is given by

`((1)/(4)x-(1)/(2))(5x^2-2x+6)\\\\=(x)/(4)(5x^2-2x+6)-(1)/(2)(5x^2-2x+6)\\\\=(5x^3)/(4)-(1)/(2)x^2+(3x)/(2)-(5x^2)/(2)+x-3\\\\=(5x^3)/(4)-(6x^2)/(2)+(5x)/(2)-3\\\\=(5x^3)/(4)-3x^2+(5x)/(2)-3`

No, Product of
`(1)/(2)x-(1)/(4)\ and\ 5x^2-2x+6` is not equal to Product of
`(1)/(4)x-(1)/(2)\ and\ 5x^2-2x+6`