Questions: Question 14 Factor completely. b^2 + 6bd + 5d^2

Solution Steps

To factor the given quadratic expression \( b^2 + 6bd + 5d^2 \), we need to find two binomials whose product gives the original expression. We look for two numbers that multiply to \( 5d^2 \) (the constant term) and add up to \( 6d \) (the coefficient of the middle term).

We start with the quadratic expression: \[ b^2 + 6bd + 5d^2 \]

To factor the quadratic expression, we look for two binomials whose product gives the original expression. The factors of \( 5d^2 \) that add up to \( 6d \) are \( d \) and \( 5d \). Therefore, we can write: \[ b^2 + 6bd + 5d^2 = (b + d)(b + 5d) \]

Final Answer