Solve (3x-4/5)(5x+1)-{left(5/3x+4right)}^2

$$(3x- \frac{ 4 }{ 5 } )(5x+1)- { \left( \frac{ 5 }{ 3 } x+4 \right) }^{ 2 }$$

Evaluate

$$\frac{110x^{2}}{9}-\frac{43x}{3}-\frac{84}{5}$$

Solution Steps

Use the distributive property to multiply 3x-\frac{4}{5} by 5x+1 and combine like terms.

$$15x^{2}-x-\frac{4}{5}-\left(\frac{5}{3}x+4\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{5}{3}x+4\right)^{2}.

$$15x^{2}-x-\frac{4}{5}-\left(\frac{25}{9}x^{2}+\frac{40}{3}x+16\right)$$

To find the opposite of \frac{25}{9}x^{2}+\frac{40}{3}x+16, find the opposite of each term.

$$15x^{2}-x-\frac{4}{5}-\frac{25}{9}x^{2}-\frac{40}{3}x-16$$

Combine 15x^{2} and -\frac{25}{9}x^{2} to get \frac{110}{9}x^{2}.

$$\frac{110}{9}x^{2}-x-\frac{4}{5}-\frac{40}{3}x-16$$

Combine -x and -\frac{40}{3}x to get -\frac{43}{3}x.

$$\frac{110}{9}x^{2}-\frac{43}{3}x-\frac{4}{5}-16$$

Subtract 16 from -\frac{4}{5} to get -\frac{84}{5}.

$$\frac{110}{9}x^{2}-\frac{43}{3}x-\frac{84}{5}$$

Expand

$$\frac{110x^{2}}{9}-\frac{43x}{3}-\frac{84}{5}$$

Solution Steps

Use the distributive property to multiply 3x-\frac{4}{5} by 5x+1 and combine like terms.

$$15x^{2}-x-\frac{4}{5}-\left(\frac{5}{3}x+4\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(\frac{5}{3}x+4\right)^{2}.

$$15x^{2}-x-\frac{4}{5}-\left(\frac{25}{9}x^{2}+\frac{40}{3}x+16\right)$$

To find the opposite of \frac{25}{9}x^{2}+\frac{40}{3}x+16, find the opposite of each term.

$$15x^{2}-x-\frac{4}{5}-\frac{25}{9}x^{2}-\frac{40}{3}x-16$$

Combine 15x^{2} and -\frac{25}{9}x^{2} to get \frac{110}{9}x^{2}.

$$\frac{110}{9}x^{2}-x-\frac{4}{5}-\frac{40}{3}x-16$$

Combine -x and -\frac{40}{3}x to get -\frac{43}{3}x.

$$\frac{110}{9}x^{2}-\frac{43}{3}x-\frac{4}{5}-16$$

Subtract 16 from -\frac{4}{5} to get -\frac{84}{5}.

$$\frac{110}{9}x^{2}-\frac{43}{3}x-\frac{84}{5}$$