Solve (2/5x+5)(1/5x+7)

$$( \frac { 2 } { 5 } x + 5 ) ( \frac { 1 } { 5 } x + 7 )$$

Evaluate

$$\frac{\left(x+35\right)\left(2x+25\right)}{25}$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{2}{5}x+5 by each term of \frac{1}{5}x+7.

$$\frac{2}{5}x\times \frac{1}{5}x+\frac{2}{5}x\times 7+5\times \frac{1}{5}x+35$$

Multiply x and x to get x^{2}.

$$\frac{2}{5}x^{2}\times \frac{1}{5}+\frac{2}{5}x\times 7+5\times \frac{1}{5}x+35$$

Multiply \frac{2}{5} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 1}{5\times 5}x^{2}+\frac{2}{5}x\times 7+5\times \frac{1}{5}x+35$$

Do the multiplications in the fraction \frac{2\times 1}{5\times 5}.

$$\frac{2}{25}x^{2}+\frac{2}{5}x\times 7+5\times \frac{1}{5}x+35$$

Express \frac{2}{5}\times 7 as a single fraction.

$$\frac{2}{25}x^{2}+\frac{2\times 7}{5}x+5\times \frac{1}{5}x+35$$

Multiply 2 and 7 to get 14.

$$\frac{2}{25}x^{2}+\frac{14}{5}x+5\times \frac{1}{5}x+35$$

Cancel out 5 and 5.

$$\frac{2}{25}x^{2}+\frac{14}{5}x+x+35$$

Combine \frac{14}{5}x and x to get \frac{19}{5}x.

$$\frac{2}{25}x^{2}+\frac{19}{5}x+35$$

Expand

$$\frac{2x^{2}}{25}+\frac{19x}{5}+35$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{2}{5}x+5 by each term of \frac{1}{5}x+7.

$$\frac{2}{5}x\times \frac{1}{5}x+\frac{2}{5}x\times 7+5\times \frac{1}{5}x+35$$

Multiply x and x to get x^{2}.

$$\frac{2}{5}x^{2}\times \frac{1}{5}+\frac{2}{5}x\times 7+5\times \frac{1}{5}x+35$$

Multiply \frac{2}{5} times \frac{1}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{2\times 1}{5\times 5}x^{2}+\frac{2}{5}x\times 7+5\times \frac{1}{5}x+35$$

Do the multiplications in the fraction \frac{2\times 1}{5\times 5}.

$$\frac{2}{25}x^{2}+\frac{2}{5}x\times 7+5\times \frac{1}{5}x+35$$

Express \frac{2}{5}\times 7 as a single fraction.

$$\frac{2}{25}x^{2}+\frac{2\times 7}{5}x+5\times \frac{1}{5}x+35$$

Multiply 2 and 7 to get 14.

$$\frac{2}{25}x^{2}+\frac{14}{5}x+5\times \frac{1}{5}x+35$$

Cancel out 5 and 5.

$$\frac{2}{25}x^{2}+\frac{14}{5}x+x+35$$

Combine \frac{14}{5}x and x to get \frac{19}{5}x.

$$\frac{2}{25}x^{2}+\frac{19}{5}x+35$$