To find the value of 36₂×14₂ using a suitable identity, we can use the following identity:
(a + b)² = a² + 2ab + b²
We can rewrite the problem as follows:
36₂×14₂ = (30₂ + 6₂)²
Using the identity above, we can expand the expression as follows:
(30₂ + 6₂)² = 30₂² + 2 * 30₂ * 6₂ + 6₂²
Substituting the values of 30₂ and 6₂ into the expression, we get:
(30₂ + 6₂)² = 900 + 360 + 36
Adding the terms, we get:
(30₂ + 6₂)² = 1296
Converting the decimal number 1296 to base 2, we get 10101100₂.
Therefore, the value of 36₂×14₂ using a suitable identity is 10101100₂.
Here is a simpler explanation:
The identity (a + b)² = a² + 2ab + b² tells us that the square of a sum is equal to the sum of the squares of the terms plus twice the product of the terms.
We can use this identity to find the product of two numbers by first converting them to base 2 and then squaring the sum of their binary representations. The product of the two numbers is then equal to the binary representation of the sum of the squares of the terms plus twice the binary representation of the product of the terms.
In this case, we want to find the product of 36₂ and 14₂. We can convert these numbers to base 2 as follows:
36₂ = 100100₂
14₂ = 1110₂
Now, we can square the sum of their binary representations as follows:
(100100₂ + 1110₂)² = 10101100₂
Finally, we can convert the decimal number 1296 to base 2 to find the product of 36₂ and 14₂:
1296₂ = 10101100₂
Therefore, the product of 36₂ and 14₂ using a suitable identity is 10101100₂.
Answers & Comments
Answer:
1 is the correct answer
A2+b2
To find the value of 36₂×14₂ using a suitable identity, we can use the following identity:
(a + b)² = a² + 2ab + b²
We can rewrite the problem as follows:
36₂×14₂ = (30₂ + 6₂)²
Using the identity above, we can expand the expression as follows:
(30₂ + 6₂)² = 30₂² + 2 * 30₂ * 6₂ + 6₂²
Substituting the values of 30₂ and 6₂ into the expression, we get:
(30₂ + 6₂)² = 900 + 360 + 36
Adding the terms, we get:
(30₂ + 6₂)² = 1296
Converting the decimal number 1296 to base 2, we get 10101100₂.
Therefore, the value of 36₂×14₂ using a suitable identity is 10101100₂.
Here is a simpler explanation:
The identity (a + b)² = a² + 2ab + b² tells us that the square of a sum is equal to the sum of the squares of the terms plus twice the product of the terms.
We can use this identity to find the product of two numbers by first converting them to base 2 and then squaring the sum of their binary representations. The product of the two numbers is then equal to the binary representation of the sum of the squares of the terms plus twice the binary representation of the product of the terms.
In this case, we want to find the product of 36₂ and 14₂. We can convert these numbers to base 2 as follows:
36₂ = 100100₂
14₂ = 1110₂
Now, we can square the sum of their binary representations as follows:
(100100₂ + 1110₂)² = 10101100₂
Finally, we can convert the decimal number 1296 to base 2 to find the product of 36₂ and 14₂:
1296₂ = 10101100₂
Therefore, the product of 36₂ and 14₂ using a suitable identity is 10101100₂.