Answer
(a) = 6x +12
(b) $=9{x^2} + 36x + 35$
Work Step by Step
a) (3x + 5) + (3x + 7) $\Longrightarrow$ This is addition of the two polynomials.
= 3x + 3x + 5 + 7
=6x +12
b) (3x + 5)(3x+7) $\Longrightarrow$ This was multiplication of two polynomials.
=3x(3x) + 3x(7) + 3x(5) + 5(7)
$=9{x^2} + 21 x + 15x + 35$
$=9{x^2} + 36x + 35$
The difference between operations in (a) and (b) is that:
(a) has the plus/add (+) sign. This means that you have to combine all like/similar terms.
(b) is multiplication. Observe that there is no sign in between. This shows that the two polynomials have to be multiplied. Similar terms and non-similar terms are all multiplied.
