Question

factor the expression.\\(10y^2 + 27y + 5\\)\\(10y^2 + 27y + 5 = \square\\)\\((type your answer in factored form.)\\)

Explanation:

Step1: Split middle term

Find two numbers that multiply to $10\times5=50$ and add to $27$. These numbers are 2 and 25.
Rewrite the expression: $10y^2 + 25y + 2y + 5$

Step2: Group terms

Group the first two and last two terms: $(10y^2 + 25y) + (2y + 5)$

Step3: Factor out GCFs

Factor GCF from each group: $5y(2y + 5) + 1(2y + 5)$

Step4: Factor common binomial

Factor out $(2y + 5)$: $(5y + 1)(2y + 5)$

Answer:

$(5y + 1)(2y + 5)$