Solve (a-2b)(a^2+2ab+4b^2)(a^3+8b^3)

$$( a - 2 b ) ( a ^ { 2 } + 2 a b + 4 b ^ { 2 } ) ( a ^ { 3 } + 8 b ^ { 3 } )$$

Evaluate

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

Solution Steps

Use the distributive property to multiply a-2b by a^{2}+2ab+4b^{2} and combine like terms.

$$\left(a^{3}-8b^{3}\right)\left(a^{3}+8b^{3}\right)$$

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

$$\left(a^{3}\right)^{2}-\left(8b^{3}\right)^{2}$$

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

$$a^{6}-\left(8b^{3}\right)^{2}$$

Expand \left(8b^{3}\right)^{2}.

$$a^{6}-8^{2}\left(b^{3}\right)^{2}$$

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

$$a^{6}-8^{2}b^{6}$$

Calculate 8 to the power of 2 and get 64.

$$a^{6}-64b^{6}$$

Expand

$$a^{6}-64b^{6}$$

Solution Steps

Use the distributive property to multiply a-2b by a^{2}+2ab+4b^{2} and combine like terms.

$$\left(a^{3}-8b^{3}\right)\left(a^{3}+8b^{3}\right)$$

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

$$\left(a^{3}\right)^{2}-\left(8b^{3}\right)^{2}$$

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

$$a^{6}-\left(8b^{3}\right)^{2}$$

Expand \left(8b^{3}\right)^{2}.

$$a^{6}-8^{2}\left(b^{3}\right)^{2}$$

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

$$a^{6}-8^{2}b^{6}$$

Calculate 8 to the power of 2 and get 64.

$$a^{6}-64b^{6}$$