Solve 15p*p+7p-3+5p

$$15 p \cdot p + 7 p - 3 + 5 p$$

Evaluate

$$3\left(5p-1\right)\left(p+1\right)$$

Solution Steps

Multiply p and p to get p^{2}.

$$15p^{2}+7p-3+5p$$

Combine 7p and 5p to get 12p.

$$15p^{2}+12p-3$$

Factor

$$3\left(5p-1\right)\left(p+1\right)$$

Solution Steps

Multiply and combine like terms.

$$15p^{2}+12p-3$$

Factor out 3.

$$3\left(5p^{2}+4p-1\right)$$

Consider 5p^{2}+4p-1. Factor the expression by grouping. First, the expression needs to be rewritten as 5p^{2}+ap+bp-1. To find a and b, set up a system to be solved.

$$a+b=4 ab=5\left(-1\right)=-5$$

Since ab is negative, a and b have the opposite signs. Since a+b is positive, the positive number has greater absolute value than the negative. The only such pair is the system solution.

$$a=-1 b=5$$

Rewrite 5p^{2}+4p-1 as \left(5p^{2}-p\right)+\left(5p-1\right).

$$\left(5p^{2}-p\right)+\left(5p-1\right)$$

Factor out p in 5p^{2}-p.

$$p\left(5p-1\right)+5p-1$$

Factor out common term 5p-1 by using distributive property.

$$\left(5p-1\right)\left(p+1\right)$$

Rewrite the complete factored expression.

$$3\left(5p-1\right)\left(p+1\right)$$