Answer :
To rewrite the equation y=(x+2)^3+4 without parentheses, we can apply the exponent to each term inside the parentheses and then simplify.
Step 1: Expand the cube power inside the parentheses.
(x+2)^3 = (x+2)(x+2)(x+2) = x(x+2)(x+2) + 2(x+2)(x+2) = x(x^2+4x+4) + 2(x^2+4x+4)
Step 2: Distribute the terms.
= x(x^2+4x+4) + 2(x^2+4x+4) = x^3 + 4x^2 + 4x + 2x^2 + 8x + 8
Step 3: Combine like terms.
= x^3 + (4x^2 + 2x^2) + (4x + 8x) + 8 = x^3 + 6x^2 + 12x + 8
Step 4: Add 4 to the result.
y = x^3 + 6x^2 + 12x + 8 + 4 = x^3 + 6x^2 + 12x + 12
Therefore, the equation y=(x+2)^3+4 without parentheses is y = x^3 + 6x^2 + 12x + 12.