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find the binomial expansion of (2+3x)^5 - (2 - 3x)^5

Sagot :

 The binomial expansion of (2+3x)^5 - (2 - 3x)^5 is 480x + 2160x^3 + 486x^5

Concept: Binomial expansion is to expand and write the terms which are equal to the natural number exponent of the sum or difference of two terms.

For two terms x and y the binomial expansion to the power of n is (x + y)n = nC0 0 xn y0 + nC1 1 xn - 1 y1 + nC2 2 xn-2 y2 + nC3.

Binomial expansion of (2+3x)^5 =32+240x+720x^2+1080x^3+810x^4+243x^5

Binomial expansion of (2-3x)^5 = 32-240x+720x^2-1080x^3+810x^4-243x^5

Combining both the expansions,=32+240x+720x^2+1080x^3+810x^4+243x^5 - (32-240x+720x^2-1080x^3+810x^4-243x^5)

= 32+240x+720x^2+1080x^3+810x^4+243x^5 - 32+ 240x - 720x^2 +1080x^3 -810x^4 +243x^5

=480x + 2160x^3 + 486x^5

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