Question

if ( ab = a^2 + 2ab + b^2 ), find ( 78 )

Explanation:

Step1: Identify a and b

Here, \( a = 7 \) and \( b = 8 \). The operation is defined as \( a * b = a^2 + 2ab + b^2 \).

Step2: Substitute values into the formula

Substitute \( a = 7 \) and \( b = 8 \) into \( a^2 + 2ab + b^2 \):
\( 7^2 + 2\times7\times8 + 8^2 \)

Step3: Calculate each term

Calculate \( 7^2 = 49 \), \( 2\times7\times8 = 112 \), and \( 8^2 = 64 \).

Step4: Sum the terms

Add the results: \( 49 + 112 + 64 = 225 \). Alternatively, notice that \( a^2 + 2ab + b^2=(a + b)^2 \), so \( (7 + 8)^2 = 15^2 = 225 \).

Answer:

225