P = a - 3 এবং $Q=a^2+3a+9$ হলে PQ এর মান নির্ণয় কর।

$4x^6{y}^3 \times 7x^4{y}^5$

$= \left(4 \times 7\right) \times \left(x^6\times x^4\right)\times \left(y^3\times y^5\right)$

$= 28 x^{6+4}. y^{3+5}$

$= 28 x^{10 }{y}^8 (Ans.)$

$21a^3{x}^2{y}^4 \times \left(-3a^2 x{y}^3\right)$

$= 21 \times (-3) \times (a^3 \times a^2) \times (x^2\times x) \times ( y^4\times y^3)$

$=-63 \times a^{3+2} \times x^{2+1} \times y^{4+3}$

$=-63 a^5.x^3.y^7$ (Ans)

$\left(- 6x^4{y}^3{z}^2\right) \times 9x^3{y}^5{z}^7$

$=(-6\times 9)\times (x^4\times x^3)\times (y^3\times y^5)\times (z^2\times z^7)$

$=-54 \times x^{4+3 }\times y^{3+5 }\times z^{2+7}$

$=-54 x^7{y}^8{z}^9$ (Ans)

$\left(- 11p^5{q}^2{r}^7\right) \times \left(- 13p^4{q}^{6}s\right)$

$=(-11)\times (-13)\times (p^5\times p^4)\times (q^2\times q^6)\times r^7\times s$

$=143 p^{5+4}\times q^{2+6}\times r^7 \times s$

$= 143 p^9 q^8 r^{7}s$ (Ans)

$(x^3+y^3)\times x^4\times y^5$

$=(x^3\times x^4\times y^5)+(y^3\times x^4\times y^5)$

$=(x^3\times x^4)\times y^5+x^4\times (y^3\times y^5)$

$=x^{3+4}\times y^5+x^4 \times y^{3+5}$

$= x^7{y}^5 + x^4{y}^8$ (Ans)

$a{b}^3\times (a^3+b^2)$

$=(a{b}^3\times a^3)+(a{b}^3\times b^2)$

$= \left(a^3 x a^3\right)\times b^3+ a \times (b^3 \times b^2)$

$=a^{1+3} \times b^3+a\times b^{3+2}=a^4{b}^3+a{b}^5$ (Ans.)