Answer:
(5x + 7)² = 25x² + 70x + 49 ⇒ C
Explanation:
The steps of solving the square binomial: (ax + b)²
1. (ax + b)² = (ax + b)(ax + b)
2. (ax + b)(ax + b) = (ax × ax) + (ax × b) + (b × ax) + (b × b) = a²x² + abx + abx + b²
3. Add the like terms ⇒ a²x² + (abx + abx) + b² = a²x² + 2abx + b²
Then (ax + b)² = a²x² + 2abx + b²
Let us use the same steps to solve the question
∵ (5x + 7)² = (5x + 7)(5x + 7)
∴ (5x + 7)(5x + 7) = (5x)(5x) + (5x)(7) + (7)(5x) + (7)(7)
∴ (5x + 7)(5x + 7) = 25x² + 35x + 35x + 49
→ Add the like terms
∵ 25x² + 35x + 35x + 49 = 25x² + (35x + 35x) + 49 = 25x² + 70x + 49
∴ (5x + 7)(5x + 7) = 25x² + 70x + 49
→ Then equate (5x + 7)² by the right side above
∴ (5x + 7)² = 25x² + 70x + 49