Question

Expand and combine like terms. (7m6 + 6)(7m6 – 6)

Answer 1

To expand the expression (7m6 + 6)(7m6 – 6), we recognize it as a difference of squares, yielding 49m12 – 36 after exponentiation and squaring. It simplifies to this form as there are no like terms to combine further.

Step-by-step explanation:

To expand and combine like terms for the expression (7m6 + 6)(7m6 – 6), we can use the FOIL method (First, Outside, Inside, Last). However, this expression is a difference of squares, a special case of FOIL. The product of a sum and difference of the same two terms is the difference of the squares of the two terms.

Applying this, we get:

• (7m6)2 – (6)2

By multiplying the exponentials, we add the exponents for the variable 'm' when multiplying like bases and thus:

• 72 × m6+6 – 62
• 49m12 – 36

Therefore, the expanded form is 49m12 – 36. No like terms are present, so the expression cannot be simplified further. We perform a mental check to ensure that the signs are correct, observing that a positive times a positive yields a positive result and a negative times a negative produces a positive result.