Question
Expand $(1+a)^6$ and verify by putting $a=2$ on both sides.
✓
Answer
$(1+a)^6={ }^6 C_0 1 a^0+{ }^6 C_1 \cdot 1 \cdot a^1+{ }^6 C_2 \cdot 1 \cdot a^2+{ }^6 C_3 \cdot 1 \cdot a^3+{ }^6 C_4 \cdot 1 \cdot a^4+{ }^6 C_5 \cdot 1 \cdot a^5+{ }^6 C_6 1 \cdot a^6$
$=1+6 a+15 a^2+20 a^3+15 a^4+6 a^5+a^6$
$\text { LHS }=(1+a)^6$
Putting $\mathrm{a}=2$.
$\text { LHS }=(1+2)^6=(3)^6=729$
$\text { RHS }=1+6 a+15 a^2+20 a^3+15 a^4+6 a^5+a^6$
Putting $\mathrm{a}=2$.
$\text { RHS }=1+6 \times 2+15(2)^2+20(2)^3+15(2)^4+6(2)^5+(2)^6$
$=1+12+(15 \times 4)+(20 \times 8)+(15 \times 16)+6(32)+64$
$=13+60+160+240+192+64$
$=729$
Hence, $LHS = RHS$
$=1+6 a+15 a^2+20 a^3+15 a^4+6 a^5+a^6$
$\text { LHS }=(1+a)^6$
Putting $\mathrm{a}=2$.
$\text { LHS }=(1+2)^6=(3)^6=729$
$\text { RHS }=1+6 a+15 a^2+20 a^3+15 a^4+6 a^5+a^6$
Putting $\mathrm{a}=2$.
$\text { RHS }=1+6 \times 2+15(2)^2+20(2)^3+15(2)^4+6(2)^5+(2)^6$
$=1+12+(15 \times 4)+(20 \times 8)+(15 \times 16)+6(32)+64$
$=13+60+160+240+192+64$
$=729$
Hence, $LHS = RHS$
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