Solve (1+2a)(1-2a)(1+4a^2)

$$( 1 + 2 a ) ( 1 - 2 a ) ( 1 + 4 a ^ { 2 } )$$

Evaluate

$$1-16a^{4}$$

Solution Steps

Use the distributive property to multiply 1+2a by 1-2a and combine like terms.

$$\left(1-4a^{2}\right)\left(1+4a^{2}\right)$$

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$1-\left(4a^{2}\right)^{2}$$

Expand \left(4a^{2}\right)^{2}.

$$1-4^{2}\left(a^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$1-4^{2}a^{4}$$

Calculate 4 to the power of 2 and get 16.

$$1-16a^{4}$$

Expand

$$1-16a^{4}$$

Solution Steps

Use the distributive property to multiply 1+2a by 1-2a and combine like terms.

$$\left(1-4a^{2}\right)\left(1+4a^{2}\right)$$

Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 1.

$$1-\left(4a^{2}\right)^{2}$$

Expand \left(4a^{2}\right)^{2}.

$$1-4^{2}\left(a^{2}\right)^{2}$$

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$1-4^{2}a^{4}$$

Calculate 4 to the power of 2 and get 16.

$$1-16a^{4}$$