Question

How do you solve an expansion?

Answer 1

`\large \boxed{560x^3}`

Explanation:

`(x+2)^7`

Expand brackets.

`(x+2) (x+2) (x+2) (x+2) (x+2) (x+2) (x+2)`

`(x^2 +4x+4) (x^2 +4x+4) (x^2 +4x+4)(x+2)`

`(x^4 +8x^3 +24x^2 +32x+16)(x^3 +6x^2 +12x+8)`

`x^7 +14x^6 +84x^5 +280x^4 +560x^3 +672x^2 +448x+128`

The fifth term is 560x³.

Answer 2

`\displaystyle\\(a+b)^n\\T_(r+1)=\binom{n}{r}a^(n-r)b^r\\\\\\(x+2)^7\\a=x\\b=2\\r+1=5\Rightarrow r=4\\n=7\\T_5=\binom{7}{4}x^(7-4)2^4\\T_5=(7!)/(4!3!)\cdot x^3\cdot16\\T_5=16\cdot (5\cdot6\cdot7)/(2\cdot3)\cdot x^3\\\\T_5=560x^3`