Question

The value of ${12}^4$ calculated using binomial expansion is

• A. 20734
• B. 20736
• C. 20732
• D. 20738

Answer 1

The correct option is B

20736

The given expression is

$(12{)}^4$

$=\left[\right(12{)}^2]$

$={\left[\right(10+2{)}^2]}^2$

$={[{10}^2+2^2+2\times 10\times 2]}^2\left[\right(a+b{)}^2=a^2+b^2+2ab]$

$={[100+4+40]}^2$

$=(144{)}^2$

$=(100+44{)}^2$

$=(100{)}^2+(44{)}^2+2\times 100\times 44\left[\right(a+b{)}^2=a^2+b^2+2ab]$

$=10,000+(40+4{)}^2+8800$

$=10,000+(40{)}^2+(4{)}^2+2\times 40\times 4+8800$

$=10,000+1600+16+320+8800$

$=20736$