(a) expand and simplify:
(2x+4)(x^2-3x+1)
To expand and simplify the expression (2x+4)(x^2-3x+1), we use the distributive property:
(2x + 4)(x^2 - 3x + 1) = 2x(x^2 - 3x + 1) + 4(x^2 - 3x + 1)
Now we can multiply each term separately:
= 2x * x^2 - 2x * 3x + 2x * 1 + 4 * x^2 - 4 * 3x + 4 * 1
= 2x^3 - 6x^2 + 2x + 4x^2 - 12x + 4
Next, we simplify by combining like terms:
= 2x^3 + (-6x^2 + 4x^2) + (2x - 12x) + 4
= 2x^3 - 2x^2 - 10x + 4
Therefore, the expanded and simplified expression is 2x^3 - 2x^2 - 10x + 4.