Multiply and Simplify.(∛x +2)(∛(x^2)-2∛x +4) Pleaseeeeee helpppppp!!!!!!! :(
Use the distributive property:
(∛x +2)(∛(x^2)-2∛x +4)
= (∛x)(∛(x^2)) + 2(∛(x^2)) + (∛x)(-2∛x) + 2(-2∛x) + 4(∛x) + 4*2
(When the same base with different exponents is multiplied, the exponents are added, also,
∛x = x^(1/3), ∛(x^2) = x^(2/3))
= (∛x)(∛(x^2)) + 2(∛(x^2)) + (∛x)(-2∛x) + 2(-2∛x) + 4(∛x) + 4*2
= x + 2*x^(2/3) - 2*x^(2/3) - 4*x^(1/3) + 4*x^(1/3) + 8
= x + 8
recall that a^3+b^3 = (a+b)(a^2-ab+b^2)
here you have a=∛x and b=2
(∛x +2)(∛(x^2)-2∛x +4) =(∛x)^3+2^3 = x+8
To multiply and simplify the expression (∛x + 2)(∛(x^2) - 2∛x + 4), you can use the distributive property of multiplication over addition.
Step 1: Apply the distributive property to multiply (∛x + 2) with each term inside (∛(x^2) - 2∛x + 4):
∛x * ∛(x^2) + ∛x * (-2∛x) + ∛x * 4 + 2 * ∛(x^2) + 2 * (-2∛x) + 2 * 4
Step 2: Simplify each term separately:
∛x * ∛(x^2) = ∛(x * x^2) = ∛(x^3) = x^(3/3) = x
∛x * (-2∛x) = -2(∛x * ∛x) = -2(∛(x * x)) = -2(∛(x^2)) = -2∛(x^2)
∛x * 4 = 4∛x
2 * ∛(x^2) = 2∛(x^2)
2 * (-2∛x) = -4∛x
2 * 4 = 8
Step 3: Combine like terms:
x + (-2∛(x^2)) - 4∛x + 4∛x + 8
The terms -2∛(x^2) and 4∛x cancel each other out, leaving us with:
x + 8
Therefore, the simplified expression is x + 8.