Expand (1+x)^5 and verify by putting x=1 on both sides. - Vidyadip

Question

Expand $(1+x)^5$ and verify by putting $x=1$ on both sides.

✓

Answer

$(1+x)^5={ }^5 C_0 \cdot 1 \cdot x^0+{ }^5 C_1 \cdot 1 \cdot x^1+{ }^5 C_2 1 x^2+{ }^5 C_3 \cdot 1 \cdot x^3+{ }^5 C_4 1 x^4+{ }^5 C_5 \cdot 1 \cdot x^5$
$=1+5 x+10 x^2+10 x^3+5 x^4+x^5$
$\text { LHS }=(1+x)^5$
Putting $x=1$,
$\text { LHS }=(1+1)^5=(2)^5=32$
$\text { RHS }=1+5 x+10 x^2+10 x^3+5 x^4+1$
Putting $x=1$.
$\mathrm{RHS}=1+5(1)+10(1)^2+10(1)^3+5(1)^4+1^5$
$=1+5+10+10+5+1=32$
Hence, $LHS = RHS$

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