are on the graph of the function. Finally, let's apply the Distributive Property. This will simplify the equation and determine the leading coefficient and degree of the polynomial function.

f (x) = (x + 2)^{2} (x + 4)^{2}

ExpandPosPerfectSquare

$(a + b)^{2} = a^{2} + 2 a b + b^{2}$

f (x) = (x^{2} + 2 x (2) + 2^{2}) (x^{2} + 2 x (4) + 4^{2})

CalcPowProd

Calculate power and product

f (x) = (x^{2} + 4 x + 4) (x^{2} + 8 x + 16)

Distr

Distribute $(x^{2} + 8 x + 16)$

f (x) = x^{2} (x^{2} + 8 x + 16) + 4 x (x^{2} + 8 x + 16) + 4 (x^{2} + 8 x + 16)

▼

Distribute

x^{2} & 8 x & 16

Distr

Distribute $x^{2}$

f (x) = x^{4} + 8 x^{3} + 16 x^{2} + 4 x (x^{2} + 8 x + 16) + 4 (x^{2} + 8 x + 16)

Distr

Distribute $4 x$

f (x) = x^{4} + 8 x^{3} + 16 x^{2} + 4 x^{3} + 32 x^{2} + 64 x + 4 (x^{2} + 8 x + 16)

Distr

Distribute $4$

f (x) = x^{4} + 8 x^{3} + 16 x^{2} + 4 x^{3} + 32 x^{2} + 64 x + 4 x^{2} + 32 x + 64

AddTerms

Add terms

f (x) = x^{4} + 12 x^{3} + 52 x^{2} + 96 x + 64

We can see now that the leading coefficient is

1,

which is a positive number. Also, the degree is

4,

which is an even number. Therefore, the end behavior is up and up. Now, let's draw the graph!

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