Final answer:
To evaluate (3x+7)(3x+7), use the identity (a+b)^2 = a^2 + 2ab + b^2, resulting in 9x^2 + 42x + 49.
Step-by-step explanation:
To evaluate the expression (3x+7)(3x+7), we can use the algebraic identity "(a+b)2 = a2 + 2ab + b2". In this case, a is 3x and b is 7.
Step 1: Square the first term: a2 = (3x)2 = 9x2.
Step 2: Multiply the two terms together and double the result: 2ab = 2(3x)(7) = 42x.
Step 3: Square the second term: b2 = 72 = 49
Putting it all together, the expression simplifies to 9x2 + 42x + 49.
Always check the answer to see if it is reasonable, which in this case it is.