2n-3n+1⋅2n2+5n+39-4n2

For a polynomial of the form ax2+bx+c, rewrite the middle term as a sum of two terms whose product is a⋅c=2⋅3=6 and whose sum is b=5.

Factor 5 out of 5n.

2n-3n+1⋅2n2+5(n)+39-4n2

Rewrite 5 as 2 plus 3

2n-3n+1⋅2n2+(2+3)n+39-4n2

Apply the distributive property.

2n-3n+1⋅2n2+2n+3n+39-4n2

2n-3n+1⋅2n2+2n+3n+39-4n2

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

2n-3n+1⋅(2n2+2n)+3n+39-4n2

Factor out the greatest common factor (GCF) from each group.

2n-3n+1⋅2n(n+1)+3(n+1)9-4n2

2n-3n+1⋅2n(n+1)+3(n+1)9-4n2

Factor the polynomial by factoring out the greatest common factor, n+1.

2n-3n+1⋅(n+1)(2n+3)9-4n2

2n-3n+1⋅(n+1)(2n+3)9-4n2

Rewrite 9 as 32.

2n-3n+1⋅(n+1)(2n+3)32-4n2

Rewrite 4n2 as (2n)2.

2n-3n+1⋅(n+1)(2n+3)32-(2n)2

Since both terms are perfect squares, factor using the difference of squares formula, a2-b2=(a+b)(a-b) where a=3 and b=2n.

2n-3n+1⋅(n+1)(2n+3)(3+2n)(3-(2n))

Multiply 2 by -1.

2n-3n+1⋅(n+1)(2n+3)(3+2n)(3-2n)

2n-3n+1⋅(n+1)(2n+3)(3+2n)(3-2n)

Cancel the common factor of n+1.

Cancel the common factor.

2n-3n+1⋅(n+1)(2n+3)(3+2n)(3-2n)

Rewrite the expression.

(2n-3)⋅2n+3(3+2n)(3-2n)

(2n-3)⋅2n+3(3+2n)(3-2n)

Cancel the common factor of 2n+3 and 3+2n.

Reorder terms.

(2n-3)⋅2n+3(2n+3)(3-2n)

Cancel the common factor.

(2n-3)⋅2n+3(2n+3)(3-2n)

Rewrite the expression.

(2n-3)⋅13-2n

(2n-3)⋅13-2n

Multiply 2n-3 and 13-2n.

2n-33-2n

Cancel the common factor of 2n-3 and 3-2n.

Factor -1 out of 2n.

-(-2n)-33-2n

Rewrite -3 as -1(3).

-(-2n)-1(3)3-2n

Factor -1 out of -(-2n)-1(3).

-(-2n+3)3-2n

Rewrite -(-2n+3) as -1(-2n+3).

-1(-2n+3)3-2n

Reorder terms.

-1(-2n+3)-2n+3

Cancel the common factor.

-1(-2n+3)-2n+3

Divide -1 by 1.

-1

-1

-1

Multiply (2n-3)/(n+1)*(2n^2+5n+3)/(9-4n^2)