Question

Use polynomial identities to multiply the expressions. Identify which identity you used. (7+9)^2

Answer 1

To multiply (7+9)^2, apply the square of a binomial identity, which results in 49 + 126 + 81 and simplifies to 256. This demonstrates how to use polynomial identities to simplify expressions efficiently.

Step-by-step explanation:

To multiply the expressions using polynomial identities, consider the identity (a + b)^2 = a^2 + 2ab + b^2. This is often referred to as the square of a binomial. Applying this identity to (7+9)^2, we treat 7 as 'a' and 9 as 'b'.

First, square the first term: 7^2 = 49.
Second, multiply the two terms together and double the result: 2*(7)(9) = 2*63 = 126.
Third, square the second term: 9^2 = 81.
Finally, add all these results together: 49 + 126 + 81 = 256.

Therefore, (7+9)^2 simplifies to 256 using the square of a binomial identity.

Steps to Solve:

1. Square the first term (7^2 = 49).
2. Multiply the two terms together and double the result (2*(7)(9) = 126).
3. Square the second term (9^2 = 81).
4. Add all resulting terms together (49 + 126 + 81 = 256).

Using this method, we can quickly and accurately multiply expressions and understand the concept behind the identity.