Solve left(50x+100right)^2+left(130xright)^2-12*20x*(50x+100)

$${ \left(50x+100 \right) }^{ 2 } + { \left(130x \right) }^{ 2 } -12 \times 20x \times (50x+100)$$

Evaluate

$$7400x^{2}-14000x+10000$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(50x+100\right)^{2}.

$$2500x^{2}+10000x+10000+\left(130x\right)^{2}-12\times 20x\left(50x+100\right)$$

Expand \left(130x\right)^{2}.

$$2500x^{2}+10000x+10000+130^{2}x^{2}-12\times 20x\left(50x+100\right)$$

Calculate 130 to the power of 2 and get 16900.

$$2500x^{2}+10000x+10000+16900x^{2}-12\times 20x\left(50x+100\right)$$

Combine 2500x^{2} and 16900x^{2} to get 19400x^{2}.

$$19400x^{2}+10000x+10000-12\times 20x\left(50x+100\right)$$

Multiply 12 and 20 to get 240.

$$19400x^{2}+10000x+10000-240x\left(50x+100\right)$$

Use the distributive property to multiply -240x by 50x+100.

$$19400x^{2}+10000x+10000-12000x^{2}-24000x$$

Combine 19400x^{2} and -12000x^{2} to get 7400x^{2}.

$$7400x^{2}+10000x+10000-24000x$$

Combine 10000x and -24000x to get -14000x.

$$7400x^{2}-14000x+10000$$

Expand

$$7400x^{2}-14000x+10000$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(50x+100\right)^{2}.

$$2500x^{2}+10000x+10000+\left(130x\right)^{2}-12\times 20x\left(50x+100\right)$$

Expand \left(130x\right)^{2}.

$$2500x^{2}+10000x+10000+130^{2}x^{2}-12\times 20x\left(50x+100\right)$$

Calculate 130 to the power of 2 and get 16900.

$$2500x^{2}+10000x+10000+16900x^{2}-12\times 20x\left(50x+100\right)$$

Combine 2500x^{2} and 16900x^{2} to get 19400x^{2}.

$$19400x^{2}+10000x+10000-12\times 20x\left(50x+100\right)$$

Multiply 12 and 20 to get 240.

$$19400x^{2}+10000x+10000-240x\left(50x+100\right)$$

Use the distributive property to multiply -240x by 50x+100.

$$19400x^{2}+10000x+10000-12000x^{2}-24000x$$

Combine 19400x^{2} and -12000x^{2} to get 7400x^{2}.

$$7400x^{2}+10000x+10000-24000x$$

Combine 10000x and -24000x to get -14000x.

$$7400x^{2}-14000x+10000$$