Finite Math Examples

Expand Using Pascal's Triangle (3x-2)^5
Step 1
Pascal's Triangle can be displayed as such:
The triangle can be used to calculate the coefficients of the expansion of by taking the exponent and adding . The coefficients will correspond with line of the triangle. For , so the coefficients of the expansion will correspond with line .
Step 2
The expansion follows the rule . The values of the coefficients, from the triangle, are .
Step 3
Substitute the actual values of and into the expression.
Step 4
Simplify each term.
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Step 4.1
Multiply by .
Step 4.2
Apply the product rule to .
Step 4.3
Raise to the power of .
Step 4.4
Anything raised to is .
Step 4.5
Multiply by .
Step 4.6
Apply the product rule to .
Step 4.7
Raise to the power of .
Step 4.8
Multiply by .
Step 4.9
Evaluate the exponent.
Step 4.10
Multiply by .
Step 4.11
Apply the product rule to .
Step 4.12
Raise to the power of .
Step 4.13
Multiply by .
Step 4.14
Raise to the power of .
Step 4.15
Multiply by .
Step 4.16
Apply the product rule to .
Step 4.17
Raise to the power of .
Step 4.18
Multiply by .
Step 4.19
Raise to the power of .
Step 4.20
Multiply by .
Step 4.21
Simplify.
Step 4.22
Multiply by .
Step 4.23
Raise to the power of .
Step 4.24
Multiply by .
Step 4.25
Multiply by .
Step 4.26
Apply the product rule to .
Step 4.27
Anything raised to is .
Step 4.28
Multiply by .
Step 4.29
Anything raised to is .
Step 4.30
Multiply by .
Step 4.31
Raise to the power of .