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

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

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

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

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

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

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

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

$AB=(x^2-y^2+z^2) \times x^3{y}^4$

$=\left(x^2{x}^3{y}^4\right)-\left(y^2{x}^3{y}^4\right)+\left(z^2{x}^3{y}^4\right)$

$=\left(x^{2+3}\times y^4\right) -\left(x^3\times y^{2+4}\right) + x^3{y}^4{z}^2$

$= x^5{y}^{4 }- x^3{y}^6 + x^3{y}^4{z}^2$ (Ans.)

(p - 3q)(3p + q)

$= p\times 3p+pq-3q \times 3p - 3q \times q$

$= 3 \times p^{1+1}+ pq - 9pq - 3q^{1+1}$

$= 3p^2-8pq-3q^2$ (Ans.)

(x - y + 1)(x + y)

$= x\times x + x\times y - y\times x - y\times x - y\times y + 1\times x + 1\times y$

$=x^{1+1}+xy-xy -y^{1+1}+x+y$

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

$=x^2-y^2+x+y$  (Ans.)

a ও b এর গুণফল = ab

$=(x^3+4x-5)(x+4)$

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

$=x^{3+1}+4x^3+4x^{1+1}+16x-5x-20$

$=x^4+4x^3+4x^2+11x-20$ (Ans.)

$PQ=(a-3)(a^2+3a+9)$

$=(a\times a^2)+(a\times 3a)+(a\times 9)-(3\times a^2)-(3\times 3a)-(3\times 9)$

$=a^{1+2}+3\times a^{1+1}+9a-3a^2-9a-27$

$=a^3+3a^2+9a-3a^2-9a-27$

$=a^3-27$ (Ans.)

$(x^6-y^4+z^2) (x^3-y^3)$

$= x.x^3-x^6.y^3-y^4.x^3 + y^4.y^3+z^2{x}^3-z^2{y}^3$

$=x^{6+3}-x^6{y}^3-x^3{y}^4+y^{4+3}+z^2{x}^3-y^3{z}^2$

$=x^9-x^6{y}^3-x^3{y}^4+y^7+z^2{x}^3-y^3{z}^2$ (Ans.)

$(x^5-y^5)(x^3+y^4)$

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

$=x^{5+3}+x^5{y}^4-x^3{y}^5-y^{5+4}$

$= x^8 + x^5 y^4- x^3{y}^5 - y^9$ (Ans.)

$pq=(x^3+1)(x^3-1)$

$=x^3\times x^3-x^3+x^3-1$

$$\begin{gathered} =x^{3+3}-1 \\ = x^6-1 \end{gathered}$$

$ab=(x^2+4) (x^2-4)$

$=x^2\times x^2-4\times x^2+4\times x^2-4\times 4$

$=x^{2+2}-4x^2+4x^2-16=x^4-16$ (Ans.)

$- 35p^6{q}^9$

$56a^5{x}^7{y}^8{p}^6$

$15x^5{y}^3{z}^4 + 20x^2{y}^7{z}^4$

$a^7{b}^5+a^4{b}^8-a^4{b}^5$

$x^{10}{y}^4- x^4{y}^{10}$

$x^2+5x-3x^2-8x+35$

$a^2-b^2- ac + bc$

$a^6– b^6$

$x^3-64$

$x^6-x^4{y}^2+x^2{y}^2-y^4-x^{2}z+y^{2}z$