Solve (1/4x+4y)(4x-1/7y)

$$( \frac { 1 } { 4 } x + 4 y ) ( 4 x - \frac { 1 } { 7 } y )$$

Evaluate

$$\frac{\left(28x-y\right)\left(x+16y\right)}{28}$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{1}{4}x+4y by each term of 4x-\frac{1}{7}y.

$$\frac{1}{4}x\times 4x+\frac{1}{4}x\left(-\frac{1}{7}\right)y+16yx+4y\left(-\frac{1}{7}\right)y$$

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

$$\frac{1}{4}x^{2}\times 4+\frac{1}{4}x\left(-\frac{1}{7}\right)y+16yx+4y\left(-\frac{1}{7}\right)y$$

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

$$\frac{1}{4}x^{2}\times 4+\frac{1}{4}x\left(-\frac{1}{7}\right)y+16yx+4y^{2}\left(-\frac{1}{7}\right)$$

Cancel out 4 and 4.

$$x^{2}+\frac{1}{4}x\left(-\frac{1}{7}\right)y+16yx+4y^{2}\left(-\frac{1}{7}\right)$$

Multiply \frac{1}{4} times -\frac{1}{7} by multiplying numerator times numerator and denominator times denominator.

$$x^{2}+\frac{1\left(-1\right)}{4\times 7}xy+16yx+4y^{2}\left(-\frac{1}{7}\right)$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{4\times 7}.

$$x^{2}+\frac{-1}{28}xy+16yx+4y^{2}\left(-\frac{1}{7}\right)$$

Fraction \frac{-1}{28} can be rewritten as -\frac{1}{28} by extracting the negative sign.

$$x^{2}-\frac{1}{28}xy+16yx+4y^{2}\left(-\frac{1}{7}\right)$$

Combine -\frac{1}{28}xy and 16yx to get \frac{447}{28}xy.

$$x^{2}+\frac{447}{28}xy+4y^{2}\left(-\frac{1}{7}\right)$$

Express 4\left(-\frac{1}{7}\right) as a single fraction.

$$x^{2}+\frac{447}{28}xy+\frac{4\left(-1\right)}{7}y^{2}$$

Multiply 4 and -1 to get -4.

$$x^{2}+\frac{447}{28}xy+\frac{-4}{7}y^{2}$$

Fraction \frac{-4}{7} can be rewritten as -\frac{4}{7} by extracting the negative sign.

$$x^{2}+\frac{447}{28}xy-\frac{4}{7}y^{2}$$

Expand

$$\frac{447xy}{28}-\frac{4y^{2}}{7}+x^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of \frac{1}{4}x+4y by each term of 4x-\frac{1}{7}y.

$$\frac{1}{4}x\times 4x+\frac{1}{4}x\left(-\frac{1}{7}\right)y+16yx+4y\left(-\frac{1}{7}\right)y$$

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

$$\frac{1}{4}x^{2}\times 4+\frac{1}{4}x\left(-\frac{1}{7}\right)y+16yx+4y\left(-\frac{1}{7}\right)y$$

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

$$\frac{1}{4}x^{2}\times 4+\frac{1}{4}x\left(-\frac{1}{7}\right)y+16yx+4y^{2}\left(-\frac{1}{7}\right)$$

Cancel out 4 and 4.

$$x^{2}+\frac{1}{4}x\left(-\frac{1}{7}\right)y+16yx+4y^{2}\left(-\frac{1}{7}\right)$$

Multiply \frac{1}{4} times -\frac{1}{7} by multiplying numerator times numerator and denominator times denominator.

$$x^{2}+\frac{1\left(-1\right)}{4\times 7}xy+16yx+4y^{2}\left(-\frac{1}{7}\right)$$

Do the multiplications in the fraction \frac{1\left(-1\right)}{4\times 7}.

$$x^{2}+\frac{-1}{28}xy+16yx+4y^{2}\left(-\frac{1}{7}\right)$$

Fraction \frac{-1}{28} can be rewritten as -\frac{1}{28} by extracting the negative sign.

$$x^{2}-\frac{1}{28}xy+16yx+4y^{2}\left(-\frac{1}{7}\right)$$

Combine -\frac{1}{28}xy and 16yx to get \frac{447}{28}xy.

$$x^{2}+\frac{447}{28}xy+4y^{2}\left(-\frac{1}{7}\right)$$

Express 4\left(-\frac{1}{7}\right) as a single fraction.

$$x^{2}+\frac{447}{28}xy+\frac{4\left(-1\right)}{7}y^{2}$$

Multiply 4 and -1 to get -4.

$$x^{2}+\frac{447}{28}xy+\frac{-4}{7}y^{2}$$

Fraction \frac{-4}{7} can be rewritten as -\frac{4}{7} by extracting the negative sign.

$$x^{2}+\frac{447}{28}xy-\frac{4}{7}y^{2}$$