Question

Using the polynomial identity (a+b)^2 = a^2 + 2ab + b^2, let's find the value of 110^2.

Let the smaller value a = _____.
a) 10
b) 11
c) 100
d) 110

And the larger value b = _____.
a) 10
b) 11
c) 100
d) 110

Then a^2 + 2ab + b^2 is _____.
a) a^2 + b^2
b) (a + b)^2
c) 2ab
d) 3ab

This can be simplified to _____.
a) (a + b)^2
b) 2ab
c) a^2 + b^2
d) a^2 + 2ab + b^2

So, 110^2 is equal to _____.
a) 121
b) 12,100
c) 11,000
d) 12

Answer 1

By expressing 110 as the sum of 100 and 10, we use the identity (a+b)^2 to find that 110^2 equals 100^2 + 2(100)(10) + 10^2, which is 12,100.

Step-by-step explanation:

To find the value of 1102 using the polynomial identity (a+b)2 = a2 + 2ab + b2, we can express 110 as the sum of two convenient numbers. We can let the smaller value a = 100 (option c) and the larger value b = 10 (option a).

Using these values, we get:

a2 + 2ab + b2 represents the expanded form of the binomial squared, so it equates to (a + b)2 (option b).

This can be simplified to a2 + 2ab + b2 without any further simplification (option d).

Therefore, 1102 is equal to 1002 + 2(100)(10) + 102, which calculates to 12,100 (option b).