Answer: To simplify the expression (x^3 - 3x^2 + 5) (2x^2 + 5x - 8), we can use the distributive property of multiplication over addition. This means that we need to multiply each term in the first expression (x^3 - 3x^2 + 5) by each term in the second expression (2x^2 + 5x - 8) and then combine like terms.
Let's break down the steps:
Step 1: Multiply the first term in the first expression (x^3) by each term in the second expression (2x^2 + 5x - 8). We get:
x^3 * 2x^2 = 2x^5
x^3 * 5x = 5x^4
x^3 * -8 = -8x^3
Step 2: Multiply the second term in the first expression (-3x^2) by each term in the second expression (2x^2 + 5x - 8). We get:
-3x^2 * 2x^2 = -6x^4
-3x^2 * 5x = -15x^3
-3x^2 * -8 = 24x^2
Step 3: Multiply the third term in the first expression (5) by each term in the second expression (2x^2 + 5x - 8). We get:
5 * 2x^2 = 10x^2
5 * 5x = 25x
5 * -8 = -40
Step 4: Now, we can combine like terms.
2x^5 + 5x^4 - 8x^3 - 6x^4 - 15x^3 + 24x^2 + 10x^2 + 25x - 40
Step 5: Simplify the expression by combining like terms.
2x^5 + (-6x^4 + 5x^4) + (-15x^3 + 24x^2 - 8x^3) + (10x^2) + (25x) + (-40)
Final answer:
2x^5 - x^4 - 23x^3 + 34x^2 + 25x - 40