Expand using the binomial theorem
-$(x+4 y)^{4}$
A) $x^{4}+16 x^{3} y+96 x^{2} y^{2}+256 x y^{3}+256 y^{4}$
B) $x^{4}+16 x^{3} y+128 x^{2} y^{2}+256 x y^{3}+256 y^{4}$
C) $x^{4}+4 x^{3} y+96 x^{2} y^{2}+128 x y^{3}+256 y^{4}$
D) $x^{4}+16 x^{3} y+96 x^{2} y^{2}+16 x y^{3}+256 y^{4}$

Question

Quizplus · Accepted Answer

The binomial theorem states that $(x+y)^n = \sum_{k=0}^{n} \binom{n}{k} x^{n-k}y^k$. Applying this to $(x+4y)^4$, we get $x^4 + 4\binom{4}{1}x^3(4y) + 6\binom{4}{2}x^2(4y)^2 + 4\binom{4}{3}x(4y)^3 + (4y)^4$, which simplifies to $x^4 + 16x^3y + 96x^2y^2 + 256xy^3 + 256y^4$.

Expand Using the Binomial Theorem - (x+4y)4(x+4 y)^{4}(x+4y)4 A) x4+16x3y+96x2y2+256xy3+256y4x^{4}+16 x^{3} y+96 x^{2} y^{2}+256 x y^{3}+256 y^{4}x4+16x3y+96x2y2+256xy3+256y4

Expand Using the Binomial Theorem
- $(x+4 y)^{4}$ A) $x^{4}+16 x^{3} y+96 x^{2} y^{2}+256 x y^{3}+256 y^{4}$