Factor 9a^2 - 42a +49

The expression 9a^2 - 42a +49 can be factored into (3a-7)^2.

Here's how to show it:
1. Find the factors of 9 and 49: 9 * 49 = 441.
2. Find two numbers that multiply to 441 and add up to -42 (the coefficient of the middle term).
The numbers are -21 and -21, since (-21) * (-21) = 441 and (-21) + (-21) = -42.
3. Use these numbers to rewrite the middle term as -21a - 21a, so 9a^2 - 42a + 49 becomes:
9a^2 - 21a - 21a + 49.
4. Group the terms to factor by grouping:
(9a^2 - 21a) - (21a - 49)
3a(3a - 7) - 7(3a - 7)
(3a - 7)(3a - 7)
(3a - 7)^2

Therefore, 9a^2 - 42a + 49 is equal to (3a-7)^2.