Use the Binomial Theorem to expand and simplify the expression. $( r + 2 ) ^ { 5 }$
A) $r ^ { 5 } + 10 r ^ { 4 } + 8 r ^ { 3 } + 80 r ^ { 2 } + 80 r + 32$
B) $r ^ { 5 } + 10 r ^ { 4 } + 36 r ^ { 3 } + 80 r ^ { 2 } + 80 r + 32$
C) $r ^ { 5 } + 10 r ^ { 4 } + 40 r ^ { 3 } + 80 r ^ { 2 } + 80 r + 32$
D) $r ^ { 5 } + 10 r ^ { 4 } + 40 r ^ { 3 } + 80 r ^ { 2 } + 72 r + 36$
E) $r ^ { 5 } + 10 r ^ { 4 } + 40 r ^ { 3 } + 80 r ^ { 2 } + 60 r + 120$

Question

Quizplus · Accepted Answer

We can use the Binomial Theorem to expand the expression as follows:
(2x + 3y)^2 = (2x)^2 + 2(2x)(3y) + (3y)^2
= 4x^2 + 12xy + 9y^2
Therefore, the expression simplifies to:
(4x^2 + 12xy + 9y^2) - (2x^2 - 6xy + 3y^2)
= 2x^2 + 18xy + 6y^2
Converting this expression to hexadecimal gives us:
11ea99db_b286_fdb4_94ac_ff2d6948013b_TB4590_11
Therefore, the correct answer is choice C.

Use the Binomial Theorem to Expand and Simplify the Expression (r+2)5( r + 2 ) ^ { 5 }(r+2)5

Use the Binomial Theorem to Expand and Simplify the Expression $( r + 2 ) ^ { 5 }$