Question

1. $5x^{2}y - x^{2} + 5y - 1$

Explanation:

Step1: Group terms

Group the first two terms and the last two terms: $(5x^{2}y - x^{2})+(5y - 1)$

Step2: Factor out common factors

Factor out $x^{2}$ from the first group and $1$ from the second group: $x^{2}(5y - 1)+1(5y - 1)$

Step3: Factor out the common binomial factor

Factor out $(5y - 1)$: $(5y - 1)(x^{2}+1)$

Answer:

$(5y - 1)(x^{2}+1)$