Use the Binomial Theorem to expand and simplify the expression. $2 ( x - 5 ) ^ { 4 } + 5 ( x - 5 ) ^ { 2 }$
A) $2 x ^ { 4 } - 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x + 1375$
B) $2 x ^ { 4 } + 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x + 1375$
C) $2 x ^ { 4 } - 40 x ^ { 3 } - 305 x ^ { 2 } - 1050 x + 1375$
D) $2 x ^ { 4 } - 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x - 1375$
E) $2 x ^ { 4 } - 40 x ^ { 3 } - 305 x ^ { 2 } - 1050 x - 1375$

Question

Use the Binomial Theorem to expand and simplify the expression.   $2 ( x - 5 ) ^ { 4 } + 5 ( x - 5 ) ^ { 2 }$  
A) $2 x ^ { 4 } - 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x + 1375$
B) $2 x ^ { 4 } + 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x + 1375$
C) $2 x ^ { 4 } - 40 x ^ { 3 } - 305 x ^ { 2 } - 1050 x + 1375$
D) $2 x ^ { 4 } - 40 x ^ { 3 } + 305 x ^ { 2 } - 1050 x - 1375$
E) $2 x ^ { 4 } - 40 x ^ { 3 } - 305 x ^ { 2 } - 1050 x - 1375$

Quizplus · Accepted Answer

The Binomial Theorem is used to expand $(x - 5)^4$ and $(x - 5)^2$. For $(x - 5)^4$, the expansion is $x^4 - 20x^3 + 150x^2 - 500x + 625$, and for $(x - 5)^2$, it is $x^2 - 10x + 25$. Multiplying these by 2 and 5 respectively and then adding them gives $2x^4 - 40x^3 + 300x^2 - 1000x + 1250 + 5x^2 - 50x + 125$, which simplifies to $2x^4 - 40x^3 + 305x^2 - 1050x + 1375$.

Use the Binomial Theorem to Expand and Simplify the Expression 2(x−5)4+5(x−5)22 ( x - 5 ) ^ { 4 } + 5 ( x - 5 ) ^ { 2 }2(x−5)4+5(x−5)2

Use the Binomial Theorem to Expand and Simplify the Expression $2 ( x - 5 ) ^ { 4 } + 5 ( x - 5 ) ^ { 2 }$