Answer:
(b + 8 + c)(b + 8 - c)
Explanation:
Factorizing the algebraic expressions using identities:
First use the algebraic identity x² + 2xy +y² = (x +y)² for the expression b² + 16b + 64.
b² + 16b + 64 = b² + 2 * b * 4 + 8²
On Comparing b² + 2 * b* 4 + 8² with x² + 2xy + y² , we get x = b & y = 8.
b² + 16b + 64 = (b + 8)²
b² + 16b + 64 - c² = (b +8)² - c²
Use Algebraic identity: x² - y² = (x + y)(x -y)
x = b +8 & y = c
= (b + 8 + c)( b + 8 - c)
Answer: b² + 16b + 64 - c² = (b + 8 + c)(b + 8 - c)