(w + 2t)(w^2 - 2wt + 4t^2)
(x + y)(x^2 -3xy + 2y^2)
=x^3 - 3x^2y + 2xy^2 + x^2y -3xy^2 + 2y^3
= x^3-2x^2y-xy^2+2y^3
To solve the multiplication of two binomials, such as (w + 2t)(w^2 - 2wt + 4t^2), you can use the distributive property.
Step 1: Distribute the first term of the first binomial (w) to every term in the second binomial (w^2, -2wt, and 4t^2).
(w * w^2) + (w * -2wt) + (w * 4t^2)
= w^3 - 2w^2t + 4wt^2
Step 2: Distribute the second term of the first binomial (2t) to every term in the second binomial (w^2, -2wt, and 4t^2).
(2t * w^2) + (2t * -2wt) + (2t * 4t^2)
= 2tw^2 - 4t^2w + 8t^3
Step 3: Combine all the terms obtained in Step 1 and Step 2.
(w^3 - 2w^2t + 4wt^2) + (2tw^2 - 4t^2w + 8t^3)
= w^3 + 2tw^2 - 2w^2t - 4t^2w + 4wt^2 + 8t^3
Simplifying the expression further, we get:
= w^3 + 2tw^2 - 2w^2t - 4t^2w + 4wt^2 + 8t^3