(a) To find the product of 1/2x-1/4 and 5x^2-2x+6, we can use the distributive property of multiplication:
(1/2x - 1/4)(5x^2 - 2x + 6)
= (1/2x)(5x^2) + (1/2x)(-2x) + (1/2x)(6) - (1/4)(5x^2) + (1/4)(2x) - (1/4)(6)
= (5/2)x^2 - x + 3 - (5/4)x + (1/2)x - (3/2)
= (5/2)x^2 - (3/4)x + 3/2
Therefore, the product of 1/2x-1/4 and 5x^2-2x+6 is (5/2)x^2 - (3/4)x + 3/2.
(b) No, the product of 1/2x-1/4 and 5x^2-2x+6 is not equal to the product of 1/4x-1/2 and 5x^2-2x+6. This is because when we expand both products using the distributive property, we get different expressions:
(1/2x - 1/4)(5x^2 - 2x + 6) = (5/2)x^2 - (3/4)x + 3/2
(1/4x - 1/2)(5x^2 - 2x + 6) = (5/4)x^2 - (7/4)x + 3
So the coefficients of the x^2 and x terms in the two products are different. Therefore, the two products are not equal.