Question

Which expression is equivalent to

Answer 1

Answer:

$\frac{(2a+1)^{2} }{50a}$

Step-by-step explanation:

$\frac{2a+1}{10a-5} * \frac{4a^{2} - 1}{10a}\\ = \frac{2a+1}{5(2a-1)} * \frac{(2a+1)(2a-1)}{10a}\\=\frac{(2a+1)^{2} }{50a}$

1.The expression given is in division so when changing to multiplication the fraction is reversed.

2.Using algebra identity $a^{2} - b^{2} = (a+b)(a-b)$.

3. Taking the common factor 5 out.

4. Finally cancelling the like terms from the numerator and denominator.