Expand and simplify $(3x - y)(y + x).$ Factorise completely $3 - 12a^2$.

1. Expand the product of the two brackets term by term.

$(3x-y)(y+x)=3x(y+x)-y(y+x)$

$=3xy+3x^2-y^2-xy$

2. Collect like terms and write the expression in simplified form.

$3xy-xy=2xy$

So,
$(3x-y)(y+x)=3x^2+2xy-y^2.$

1. Extract the common factor from both terms.

$3-12a^2=3(1-4a^2)$

2. Factorise the difference of two squares completely.

$1-4a^2=1^2-(2a)^2=(1-2a)(1+2a)$

So,
$3-12a^2=3(1-2a)(1+2a)$