Question

Factorize each of the following algebraic expression:
49 − a² + 8ab − 16b²

Answer 1

\[49 - a^2 + 8ab - 16 b^2 \]
\[ = 49 - ( a^2 - 8ab + 16 b^2 )\]
\[ = 49 - [ a^2 - 2 \times a \times 4b + (4b )^2 ]\]
\[ = 7^2 - (a - 4b )^2 \]
\[ = [7 - (a - 4b)][7 + (a - 4b)]\]
\[ = (7 - a + 4b)(7 + a - 4b)\]
\[ = - (a - 4b - 7)(a - 4b + 7)\]
\[ = - (a - 4b + 7)(a - 4b - 7)\]