Use Pascal's Triangle to complete the expansion of (w + x)^6. w^6 + 6w^5x + ____w^4x^2 + 20w^3x^3 + 15w^2x^4 + 6wx^5 + x^6

Look at Pascal's Triangle: Look at Pascal's Triangle to find the coefficients for the expansion of (w + x)^6. The 7th row (since we start counting from 0) is 1, 6, 15, 20, 15, 6, 1.Identify coefficients needed: We already have the coefficients for w^6, w^5x, w^3x^3, w^2x^4, wx^5, and x^6. We need the coefficient for w^4x^2.Calculate coefficient for w^4x^2: The coefficient for w^4x^2 is the 4th number in the 7th row of Pascal's Triangle, which is 15.

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Use Pascal's Triangle to complete the expansion of $(w + x)^6$ . $\newline$ $w^6 + 6w^5x + \_\_\_\_w^4x^2 + 20w^3x^3 + 15w^2x^4 + 6wx^5 + x^6$

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Precalculus

Pascal's triangle and the Binomial Theorem

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Q. Use Pascal's Triangle to complete the expansion of

(w + x)^6

\newline

w^6 + 6w^5x + \_\_\_\_w^4x^2 + 20w^3x^3 + 15w^2x^4 + 6wx^5 + x^6

Look at Pascal's Triangle: Look at Pascal's Triangle to find the coefficients for the expansion of $(w + x)^6$ . The $7$ th row (since we start counting from $0$ ) is $1, 6, 15, 20, 15, 6, 1$ .
Identify coefficients needed: We already have the coefficients for $w^6$ , $w^5x$ , $w^3x^3$ , $w^2x^4$ , $wx^5$ , and $x^6$ . We need the coefficient for $w^4x^2$ .
Calculate coefficient for $w^4x^2$ : The coefficient for $w^4x^2$ is the $4$ th number in the $7$ th row of Pascal's Triangle, which is $15$ .