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Use Pascal’s triangle to expand the binomia
l (a + b)^5.
To expand (a + b)^5 using Pascal's triangle, we look at the 6th row of Pascal's triangle (since we start counting rows at 0).
Pascal's triangle:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
The coefficients of (a + b)^5 will be the numbers in the 6th row of Pascal's triangle: 1 5 10 10 5 1.
Now, we need to apply these coefficients when expanding the binomial:
(a + b)^5 = 1(a^5) + 5(a^4)(b) + 10(a^3)(b^2) + 10(a^2)(b^3) + 5(a)(b^4) + 1(b^5)
So, (a + b)^5 = a^5 + 5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + b^5.
Therefore, the expanded form of (a + b)^5 is a^5 + 5a^4b + 10a^3b^2 + 10a^2b^3 + 5ab^4 + b^5.