Question

What is 109² using the polynomial identity (a+b)²=a²+2ab+b²? Drag and drop the correct responses into the boxes. 1⁹⁰⁹⁰⁹⁰⁹⁴²+2⋅4³³+³³²⁹²+2⋅9¹⁰⁰+1⁰⁰²³³¹¹⁸⁸¹¹⁰⁹²⁴⁹ + 1⁰⁰. Let the smaller value a = Response area and the larger value b = Response area. Then a²+2ab+b² is Response area. This can be simplified to Response area. So, 109² is equal to Response area.

Answer 1

To calculate 109², we use (a+b)² = a² + 2ab + b² with a = 100 and b = 9, resulting in 10000 + 1800 + 81, which simplifies to 11881.

Step-by-step explanation:

To calculate 109² using the polynomial identity (a+b)² = a² + 2ab + b², let's identify a and b in the number 109. We can break 109 into 100 + 9, which means a = 100 and b = 9. Thus, we apply the identity:

a² = 100² = 10000

2ab = 2 × 100 × 9 = 1800

b² = 9² = 81

Putting it all together, we get:

(100+9)² = 10000 + 1800 + 81.

After adding these together, the simplified result is:

11881

Therefore, 109² is equal to 11881.