The number of terms containing the polynomial $\left(5+7x\right)\left(7x^{2}y+3y\right)$  is

$=5\left(7x^{2}y+3y\right)+7x\left(7x^{2}y+3y\right)$

$=35x^{2}y+15y+49x^{3}y+21xy$

(or)

Number of terms in $\left(5+7x\right)=2$

Number of terms in $\left(7x^{2}y+3y\right)=2$

$\therefore$  Total number of terms $=2\times 2=4$

(It satisfies only, when the terms are not same in two polynomials)

For example,

Number of terms of $\left(x+1\right)\left(x+2\right)$  is

$\left(x+1\right)\left(x+2\right)=x\left(x+2\right)+1\left(x+2\right)$

$=x^2+2x+x+2$

$=x^2+3x+2$

$\therefore$  Number of terms $=3$

But for the above problem me take $2\times 2=4$ .

In $\left(x+1\right)\left(x+2\right)$ , variable same and degree same. So we can’t take here $2\times 2$ .