How do you use the binomial theorem to expand and simplify the expression $2 {(x - 3)}^{4} + 5 {(x - 3)}^{2}$ $2(x-3)^4+5(x-3)^2$ ?

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How do you use the binomial theorem to expand and simplify the expression $2 {(x - 3)}^{4} + 5 {(x - 3)}^{2}$ $2(x-3)^4+5(x-3)^2$ ?

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Answer 1 · 2017-11-30T05:19:19

$2 x^{4} - 24 x^{3} + 113 x^{2} - 246 x + 126$ $2x^4-24x^3+113x^2-246x+126$

Explanation:

The first term expansion:
$2 (x^{4} - 4 (3) x^{3} + 6 (3^{2}) x^{2} - 4 (3^{3}) x + 3^{4})$ $2(x^4-4(3)x^3+6(3^2)x^2-4(3^3)x+3^4)$
$= 2 x^{4} - 24 x^{3} + 108 x^{2} - 216 x + 81$ $=2x^4-24x^3+108x^2-216x+81$

The second term expansion:
$5 (x^{2} - 2 (3) x + 3^{2})$ $5(x^2-2(3)x+3^2)$
$= 5 x^{2} - 30 x + 45$ $=5x^2-30x+45$

Add the 2 terms:
$2 x^{4} - 24 x^{3} + 113 x^{2} - 246 x + 126$ $2x^4-24x^3+113x^2-246x+126$

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How do you use the binomial theorem to expand and simplify the expression $2 {(x - 3)}^{4} + 5 {(x - 3)}^{2}$ $2(x-3)^4+5(x-3)^2$ ?

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How do you use the binomial theorem to expand and simplify the expression $2 {(x - 3)}^{4} + 5 {(x - 3)}^{2}$ $2(x-3)^4+5(x-3)^2$ ?