Question

Factor the expression 100x^2 - 49 using imaginary numbers.

a) (10x + 7i)(10x - 7i)
b) (5x + 7i)(20x - 7i)
c) (10x + 7)(10x - 7)
d) (5x + 7)(20x - 7)

Answer 1

To factor the expression 100x^2 - 49 using imaginary numbers, we can use the difference of squares formula. The correct answer is (10x + 7i)(10x - 7i).

Step-by-step explanation:

To factor the expression 100x^2 - 49 using imaginary numbers, we can use the difference of squares formula. This formula states that a^2 - b^2 can be factored as (a + b)(a - b).

Applying this formula to our expression, we have:

• 100x^2 - 49 = (10x)^2 - 7^2
• Using the difference of squares formula, we obtain (10x + 7)(10x - 7).

Therefore, the correct answer is option a) (10x + 7i)(10x - 7i).