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What is the binomial expansion of (x + 2)4? a. x4 + 4x3 + 6x2 + 4x + 1 b. 8x3 + 24x2 + 32x c. x4 + 8x3 + 24x2 + 32x + 16 d. 2x4 + 8x3 + 12x2 + 8x + 2

Respuesta :

Explanation:

Write out the 5th row of Pascal's triangle as a sequence:

1,4,6,4,1

Write out the powers of 2 from 24 down to 20:

16,8,4,2,1

Multiply the two sequences together to get:

16,32,24,8,1

These are the coefficients of the binomial expansion:

(2+x)4=16+32x+24x2+8x3+x4

Answer:

[tex]x^4+8x^3+24x^2+32x+16[/tex]

Step-by-step explanation:

[tex](x + 2)^4[/tex]

USe pascals triangle

WE need to 5th row in pascals triangle because we have exponent 4 (1, 4,6,4,1)

[tex]x^{n-i} y^i[/tex] where i ranges from 0 to 4

[tex]1x^4(2)^0 + 4x^3(2)^1 + 6 x^2(2)^2 + 4x^1(2)^3+1x^0(2)^4[/tex]

[tex]x^4+8x^3+24x^2+32x+16[/tex]

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