Expand (x+2y)"2", to four terms.

Question

Expand (x+2y)"2", to four terms.

Asked on March 26, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-03-26T09:42:46.581Z

Step 1: Use the double angle identity for sine, $\sin 2x = 2 \sin x \cos x$, to rewrite the integrand. $$ \int \frac{\sin 2x}{\cos x} \, dx = \int \frac{2 \sin x \cos x}{\cos x} \, dx $$ Step 2: Simplify the integrand by canceling out $\cos x$. $$ \int 2 \sin x \, dx $$ Step 3: Integrate the simplified expression. The integral of $\sin x$ is $-\cos x$. $$ 2 \int \sin x \, dx = 2(-\cos x) + C $$ Step 4: Write the final answer. $$ -2 \cos x + C $$ The final answer is $\boxed{-2 \cos x + C}$.

Accepted Answer · 2026-03-26T09:42:46.581Z

Step 1: Use the double angle identity for sine, $\sin 2x = 2 \sin x \cos x$, to rewrite the integrand. $$ \int \frac{\sin 2x}{\cos x} \, dx = \int \frac{2 \sin x \cos x}{\cos x} \, dx $$ Step 2: Simplify the integrand by canceling out $\cos x$. $$ \int 2 \sin x \, dx $$ Step 3: Integrate the simplified expression. The integral of $\sin x$ is $-\cos x$. $$ 2 \int \sin x \, dx = 2(-\cos x) + C $$ Step 4: Write the final answer. $$ -2 \cos x + C $$ The final answer is $\boxed{-2 \cos x + C}$.