Solve (0,1a^3-1)(0,1a^3+1)

$$( 0,1 a ^ { 3 } - 1 ) ( 0,1 a ^ { 3 } + 1 )$$

Evaluate

$$\frac{a^{6}}{100}-1$$

Solution Steps

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.

$$\left(0,1a^{3}\right)^{2}-1$$

Expand \left(0,1a^{3}\right)^{2}.

$$0,1^{2}\left(a^{3}\right)^{2}-1$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$0,1^{2}a^{6}-1$$

Calculate 0,1 to the power of 2 and get 0,01.

$$0,01a^{6}-1$$

Expand

$$\frac{a^{6}}{100}-1$$

Solution Steps

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.

$$\left(0,1a^{3}\right)^{2}-1$$

Expand \left(0,1a^{3}\right)^{2}.

$$0,1^{2}\left(a^{3}\right)^{2}-1$$

To raise a power to another power, multiply the exponents. Multiply 3 and 2 to get 6.

$$0,1^{2}a^{6}-1$$

Calculate 0,1 to the power of 2 and get 0,01.

$$0,01a^{6}-1$$