Question

Which polynomial identity will prove that (4 + 2)(4 + 5) = 54

Answer 1

Binomial Multiplication

Difference of Cubes

Difference of Squares

Sum of Cubes

Answer 2

First: some examples:

(4 + 2)(4 - 2) = 16 - 4: The difference of squares is 16 - 4.
Note how (4+2)(4-2)=16-4)=12.

(4 + 2)(4 + 2)= 4^2 + 2(8) + 4 = 16 + 16 + 16 = 3(16) = 48 (Binomial multiplication)

(4 + 2)(4 + 3) = 16 + 8 + 12 + 6 = 42 (Binomial mult.)

(a+b)^3 = (a+b)(a^2 -ab + b^2) => (2)^3+(3)^3) = (2+3)(2^2 - (2)(3) + 3^2) (Sum of cubes)

Which of these seems likeliest to be illustrated by (4+2)(4+5)=54?

Answer 3

umm binomial multiplication

Answer 4

Does that work for you? Have you actually tried multiplying out

(4+2)(4+5), and then multiplying out the equivalent (6)(9)?