# Without actually writing the formula, explain how to expand (x + 3)^{7} using the binomial theorem.

**Solution:**

Given, the expression is (x + 3)^{7}

We have to expand the given expression without using the binomial theorem.

**Step 1:**

To write the coefficients of the 8 terms, either start with a combination of 7 things taken 0 at a time and continue to 7 things taken 7 at a time or use the 7th row of Pascal’s triangle.

**Step 2:**

For the first term, write x to the 7^{th} power and 3 to the power 0.

Then decrease the power on x and increase the power on y until you reach x to the 0 and y to the 7.

**Step 3:**

Simplify by evaluating the coefficients and powers of 3.

Therefore, the term (x + 3)^{7} can be expanded without using the formula using binomial theorem by the above method.

## Without actually writing the formula, explain how to expand (x + 3)^{7} using the binomial theorem.

**Summary:**

Without actually writing the formula, the above method can be used to expand (x + 3)^{7} using the binomial theorem.

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