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 7th 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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