Question

Use polynomial identities to multiply (5 - 4x3)(5 + 4x3). What identity did you use?

A. Difference of cubes identity
B. Difference of squares identity
C. Binomial Theorem
D. Square of a sum identity

Answer 1

The expression (5 - 4x3)(5 + 4x3) can be simplified using the difference of squares identity, which results in 25 - 16x6.

Step-by-step explanation:

Using Polynomial Identities to Multiply

To multiply the expression (5 - 4x3)(5 + 4x3), we can apply the difference of squares identity, which states that (a - b)(a + b) = a2 - b2. Applying this identity to our expression, where a = 5 and b = 4x3, gives us:

52 - (4x3)2

25 - 16x6

The difference of squares identity is therefore the identity used to simplify this polynomial multiplication.

Answer 2

`\textit{difference of squares} \\\\ (a-b)(a+b) = a^2-b^2 \\\\[-0.35em] ~\dotfill\\\\ (5-4x^3)(5+4x^3)\implies [(5)^2-(4x^3)^2]\implies [(5^2)-(4^2x^(3\cdot 2))] \\\\[-0.35em] ~\dotfill\\\\ ~\hfill 25-16x^6~\hfill`