Determine if the function is odd, even, or neither in order to find the symmetry.

1. If odd, the function is symmetric about the origin.

2. If even, the function is symmetric about the y-axis.

Find by substituting for all occurrence of in .

Rewrite as .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Add and .

Apply the distributive property.

Simplify.

Multiply by .

Multiply by .

Simplify each term.

Apply the product rule to .

Raise to the power of .

Multiply by .

Expand by multiplying each term in the first expression by each term in the second expression.

Simplify terms.

Simplify each term.

Multiply by by adding the exponents.

Move .

Use the power rule to combine exponents.

Add and .

Multiply by .

Multiply by by adding the exponents.

Move .

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Multiply by .

Multiply by .

Subtract from .

Check if .

Since , the function is not even.

The function is not even

The function is not even

Find .

Rewrite as .

Expand using the FOIL Method.

Apply the distributive property.

Apply the distributive property.

Apply the distributive property.

Simplify and combine like terms.

Simplify each term.

Multiply by .

Move to the left of .

Multiply by .

Subtract from .

Apply the distributive property.

Simplify.

Multiply by .

Multiply by .

Expand by multiplying each term in the first expression by each term in the second expression.

Simplify terms.

Simplify each term.

Multiply by by adding the exponents.

Move .

Use the power rule to combine exponents.

Add and .

Multiply by .

Multiply by by adding the exponents.

Move .

Multiply by .

Raise to the power of .

Use the power rule to combine exponents.

Add and .

Multiply by .

Multiply by .

Simplify terms.

Subtract from .

Apply the distributive property.

Simplify.

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Multiply by .

Since , the function is not odd.

The function is not odd

The function is not odd

The function is neither odd nor even

Since the function is not odd, it is not symmetric about the origin.

No origin symmetry

Since the function is not even, it is not symmetric about the y-axis.

No y-axis symmetry

Since the function is neither odd nor even, there is no origin / y-axis symmetry.

Function is not symmetric

Find the Symmetry f(x)=-4(x-2)^2(x^2-1)