Answer:
(8x + 3)²
Explanation:
Since our polynomial is 64x² + 48x + 9, we multiply 64x² by 9 to get 64x² × 9 = 576x² since we cannot simplify the expression any further.
Next, we need to find the factors of 576x² that add up to give 48x, these are 24x and 24x.
So the expression is re-written as
64x² + 48x + 9 = 64x² + 24x + 24x + 9
Writing out all the common factors, we have,
64x² + 48x + 9 = 8x × 8x + 3 × 8x + 3 × 8x + 3 × 3
Factorizing we have
64x² + 48x + 9 = 8x(8x + 3) + 3(8x + 3)
64x² + 48x + 9 = (8x + 3)(8x + 3)
64x² + 48x + 9 = (8x + 3)²