Question

Evaluate: ${(\frac{2x}{5}+\frac{3y}{4}-\frac{4z}{7})}^2$

• A. $\frac{4x^2}{25}+\frac{9y^2}{16}-\frac{16z^2}{49}+\frac{3}{5}xy-\frac{6}{7}yz-\frac{16}{35}zx$
• B. $\frac{4x^2}{25}+\frac{9y^2}{16}+\frac{16z^2}{49}+\frac{3}{5}xy-\frac{6}{7}yz-\frac{16}{35}zx$
• C. $\frac{4x^2}{25}+\frac{3y^2}{16}+\frac{16z^2}{49}+\frac{3}{5}xy-\frac{6}{7}yz-\frac{16}{35}zx$
• D. $\frac{4x^2}{15}+\frac{9y^2}{16}+\frac{16z^2}{49}+\frac{3}{5}xy-\frac{6}{7}yz-\frac{16}{35}zx$

Answer 1

The correct option is B $\frac{4x^2}{25}+\frac{9y^2}{16}+\frac{16z^2}{49}+\frac{3}{5}xy-\frac{6}{7}yz-\frac{16}{35}zx$

${(\frac{2x}{5}+\frac{3y}{4}-\frac{4z}{7})}^2$

We know that

$(a+b+c{)}^2=a^2+b^2+c^2+2ab+2bc+2ca$

$=(\frac{2x}{5}{)}^2+(\frac{3y}{4}{)}^2+(-\frac{4z}{7}{)}^2+2(\frac{2x}{5}\left)\right(\frac{3y}{4})+2(\frac{3y}{4}\left)\right(-\frac{4z}{7})+2(-\frac{4z}{7}\left)\right(\frac{2x}{5})$

$=\frac{4x^2}{25}+\frac{9y^2}{16}+\frac{16z^2}{49}+\frac{3}{5}xy-\frac{6}{7}yz-\frac{16}{35}zx$