Solve 206(2a+3a)(-a)^2+(2a)^3-a(5a^2-7a^2)

$$206 ( 2 a + 3 a ) ( - a ) ^ { 2 } + ( 2 a ) ^ { 3 } - a ( 5 a ^ { 2 } - 7 a ^ { 2 } )$$

Evaluate

$$1040a^{3}$$

Solution Steps

Combine 2a and 3a to get 5a.

$$206\times 5a\left(-a\right)^{2}+\left(2a\right)^{3}-a\left(5a^{2}-7a^{2}\right)$$

Multiply 206 and 5 to get 1030.

$$1030a\left(-a\right)^{2}+\left(2a\right)^{3}-a\left(5a^{2}-7a^{2}\right)$$

Calculate -a to the power of 2 and get a^{2}.

$$1030aa^{2}+\left(2a\right)^{3}-a\left(5a^{2}-7a^{2}\right)$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$1030a^{3}+\left(2a\right)^{3}-a\left(5a^{2}-7a^{2}\right)$$

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

$$1030a^{3}+2^{3}a^{3}-a\left(5a^{2}-7a^{2}\right)$$

Calculate 2 to the power of 3 and get 8.

$$1030a^{3}+8a^{3}-a\left(5a^{2}-7a^{2}\right)$$

Combine 1030a^{3} and 8a^{3} to get 1038a^{3}.

$$1038a^{3}-a\left(5a^{2}-7a^{2}\right)$$

Combine 5a^{2} and -7a^{2} to get -2a^{2}.

$$1038a^{3}-a\left(-2\right)a^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$1038a^{3}-a^{3}\left(-2\right)$$

Combine 1038a^{3} and -a^{3}\left(-2\right) to get 1040a^{3}.

$$1040a^{3}$$

Expand

$$1040a^{3}$$

Solution Steps

Combine 2a and 3a to get 5a.

$$206\times 5a\left(-a\right)^{2}+\left(2a\right)^{3}-a\left(5a^{2}-7a^{2}\right)$$

Multiply 206 and 5 to get 1030.

$$1030a\left(-a\right)^{2}+\left(2a\right)^{3}-a\left(5a^{2}-7a^{2}\right)$$

Calculate -a to the power of 2 and get a^{2}.

$$1030aa^{2}+\left(2a\right)^{3}-a\left(5a^{2}-7a^{2}\right)$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$1030a^{3}+\left(2a\right)^{3}-a\left(5a^{2}-7a^{2}\right)$$

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

$$1030a^{3}+2^{3}a^{3}-a\left(5a^{2}-7a^{2}\right)$$

Calculate 2 to the power of 3 and get 8.

$$1030a^{3}+8a^{3}-a\left(5a^{2}-7a^{2}\right)$$

Combine 1030a^{3} and 8a^{3} to get 1038a^{3}.

$$1038a^{3}-a\left(5a^{2}-7a^{2}\right)$$

Combine 5a^{2} and -7a^{2} to get -2a^{2}.

$$1038a^{3}-a\left(-2\right)a^{2}$$

To multiply powers of the same base, add their exponents. Add 1 and 2 to get 3.

$$1038a^{3}-a^{3}\left(-2\right)$$

Combine 1038a^{3} and -a^{3}\left(-2\right) to get 1040a^{3}.

$$1040a^{3}$$