Solve left(-4a+60right)left(-2a^2+100cright)+left(-2a^2+60aright)left(-4a+100right)

$$\left( -4a+60 \right) \left( -2 { a }^{ 2 } +100c \right) + \left( -2 { a }^{ 2 } +60a \right) \left( -4a+100 \right)$$

Evaluate

$$16\left(a^{3}-35a^{2}-25ac+375a+375c\right)$$

Solution Steps

Use the distributive property to multiply -4a+60 by -2a^{2}+100c.

$$8a^{3}-400ac-120a^{2}+6000c+\left(-2a^{2}+60a\right)\left(-4a+100\right)$$

Use the distributive property to multiply -2a^{2}+60a by -4a+100 and combine like terms.

$$8a^{3}-400ac-120a^{2}+6000c+8a^{3}-440a^{2}+6000a$$

Combine 8a^{3} and 8a^{3} to get 16a^{3}.

$$16a^{3}-400ac-120a^{2}+6000c-440a^{2}+6000a$$

Combine -120a^{2} and -440a^{2} to get -560a^{2}.

$$16a^{3}-400ac-560a^{2}+6000c+6000a$$

Expand

$$16a^{3}-560a^{2}-400ac+6000a+6000c$$

Solution Steps

Use the distributive property to multiply -4a+60 by -2a^{2}+100c.

$$8a^{3}-400ac-120a^{2}+6000c+\left(-2a^{2}+60a\right)\left(-4a+100\right)$$

Use the distributive property to multiply -2a^{2}+60a by -4a+100 and combine like terms.

$$8a^{3}-400ac-120a^{2}+6000c+8a^{3}-440a^{2}+6000a$$

Combine 8a^{3} and 8a^{3} to get 16a^{3}.

$$16a^{3}-400ac-120a^{2}+6000c-440a^{2}+6000a$$

Combine -120a^{2} and -440a^{2} to get -560a^{2}.

$$16a^{3}-400ac-560a^{2}+6000c+6000a$$