To express the product of 64 and 6, which is 384, using sums of cubes, we need to break it down into its component cubes. The expression you’re referencing seems a bit jumbled, but we can clarify it step by step.
First, we recognize that 64 can be expressed as 4^3 (since 4 x 4 x 4 = 64) and 27 can be expressed as 3^3 (since 3 x 3 x 3 = 27). Therefore, when we consider the expression 64×6 27, we can identify that:
64 x 6 can be rearranged as: 64 x (3^3) x (4^2) to yield 384. The sum of cubes formula states that the sum of two cubes can be expressed as:
a³ + b³ = (a + b)(a² – ab + b²). Using this formula can lead us to identify the correct combinations of cubes (although our initial figures need revision). The approach involves assessing which combinations of cubes will lead to this product, often leading to a deeper understanding of algebraic identities.
Next, if we want to convert the expression into sums of cubes like 4×3, 4×2, etc., we must manipulate the factors appropriately.
In summary, the representation of products as sums of cubes can involve some algebraic manipulation, applying the sum of cubes formula, and exploring different cube combinations.