Question

1. expand the binomial $(x - 4)^4$ by applying pascals triangle.

1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
$x^4 - 12x^3 + 12x^2 - 256x$
$x^4 - 16x^3 + 96x^2 - 256x + 256$
$-4x^4 - 16x^3 + 96x^2 - 128x + 256$
$x^4 - 8x^3 + 48x^2 - 128x + 256$

Explanation:

Step1: Recall binomial expansion formula

The binomial expansion of \((a + b)^n=\sum_{k = 0}^{n}\binom{n}{k}a^{n - k}b^{k}\). For \((x-4)^4\), \(a=x\), \(b=-4\), \(n = 4\). The coefficients from Pascal's triangle for \(n = 4\) are \(1,4,6,4,1\).

Step2: Apply the formula

$$
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$$

Answer:

\(x^{4}-16x^{3}+96x^{2}-256x + 256\) (the second option)