Solve (-700-42k)^2-4(490)(300+k^2+20k)

$$( - 700 - 42 k ) ^ { 2 } - 4 ( 490 ) ( 300 + k ^ { 2 } + 20 k )$$

Evaluate

$$-196k^{2}+19600k-98000$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-700-42k\right)^{2}.

$$490000+58800k+1764k^{2}-4\times 490\left(300+k^{2}+20k\right)$$

Multiply 4 and 490 to get 1960.

$$490000+58800k+1764k^{2}-1960\left(300+k^{2}+20k\right)$$

Use the distributive property to multiply -1960 by 300+k^{2}+20k.

$$490000+58800k+1764k^{2}-588000-1960k^{2}-39200k$$

Subtract 588000 from 490000 to get -98000.

$$-98000+58800k+1764k^{2}-1960k^{2}-39200k$$

Combine 1764k^{2} and -1960k^{2} to get -196k^{2}.

$$-98000+58800k-196k^{2}-39200k$$

Combine 58800k and -39200k to get 19600k.

$$-98000+19600k-196k^{2}$$

Expand

$$-196k^{2}+19600k-98000$$

Solution Steps

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(-700-42k\right)^{2}.

$$490000+58800k+1764k^{2}-4\times 490\left(300+k^{2}+20k\right)$$

Multiply 4 and 490 to get 1960.

$$490000+58800k+1764k^{2}-1960\left(300+k^{2}+20k\right)$$

Use the distributive property to multiply -1960 by 300+k^{2}+20k.

$$490000+58800k+1764k^{2}-588000-1960k^{2}-39200k$$

Subtract 588000 from 490000 to get -98000.

$$-98000+58800k+1764k^{2}-1960k^{2}-39200k$$

Combine 1764k^{2} and -1960k^{2} to get -196k^{2}.

$$-98000+58800k-196k^{2}-39200k$$

Combine 58800k and -39200k to get 19600k.

$$-98000+19600k-196k^{2}$$