Question

Expand: $(x+3)(x+5)(x+2)$
$\left[2\right]$

Answer 1

Given
$(x+3)(x+5)(x+2)$

Comparing this with $(x+a)(x+b)(x+c)$,

we get $x=x,a=3,b=5,c=2$
$\left[1\right]$

$(x+a)(x+b)(x+c)=x^3+(a+b+c)x^2+(ab+bc+ca)x+abc$

$(x+3)(x+5)(x+2)=(x{)}^3+(3+5+2\left)\right(x{)}^2+(3\times 5+5\times 2+2\times 3)x+\left(3\right)\left(5\right)\left(2\right)$
$=x^3+10x^2+(15+10+6)x+30$

$(x+3)(x+5)(x+2)=x^3+10x^2+31x+30$
$\left[1\right]$