Simplify: (4x + 5)(4x2 + x - 4)
use the distributive property
= 16x^2 + 4x^2 - 16x + 20x^2 + 5x - 20
collect all like terms and simplify
16x+8x+4x^2-16x+20+10+5x-20therefore 4x^2+8x+5x+10 4x^2+13x+10
To simplify the expression (4x + 5)(4x^2 + x - 4), we need to use the distributive property of multiplication. This property states that when you have a sum multiplied by another number, you distribute the multiplication to each term in the sum.
Step 1: Distribute the first term of the first parenthesis to all three terms of the second parenthesis:
(4x + 5)(4x^2 + x - 4)
= 4x * 4x^2 + 4x * x + 4x * -4 + 5 * 4x^2 + 5 * x + 5 * -4
Step 2: Simplify each term:
16x^3 + 4x^2 + (-16x) + 20x^2 + 5x + (-20)
Step 3: Combine like terms:
16x^3 + (4x^2 + 20x^2) + (-16x + 5x) + (-20)
= 16x^3 + 24x^2 - 11x - 20
So, (4x + 5)(4x^2 + x - 4) simplifies to 16x^3 + 24x^2 - 11x - 20.