Explanation: गुणाकार/भागाकार
1) (3x+1)(2x+5) = ?
Explanation: \[3x(2x+5)+1(2x+5)\\ 6x^{2}+15x+2x+5\\ 6x^{2}+17x+5\\\]
2) \[\frac{6x^2 y^3}{15xy^2 z} = ?\]
Explanation: \[\frac{3\times 2\times x\times x\times y\times y\times y}{3\times 5\times x\times y\times y\times z}= \frac{2xy}{5z}\]
3) \[\frac{x^2-36}{x^2+10x+24} = ?\]
Explanation: \[\frac{x^2-6^2}{x^2+10x+24}\\ \: \: \: \:\rightarrow a2-b2 = (a+b)(a-b)\\ \frac{(x-6)(x+6)}{(x+6)(x+4)}=\frac{x-6}{x+4}\]
4) \[\frac{2x^2-x-10}{2x^2-11x+15} = ?\]
Explanation: \[\frac{(x+2)(2x-5)}{(x-3)(2x-5)} (अवयव पाडले)\\ \frac{x+2}{x-3}\]
5) \[\frac{4x^2-9y^2}{(2x+3y)(4x-9y)} = ?\]
Explanation: \[\frac{(2x)^2-(3y)^2}{(2x+3y)(4x-9y)}\\ \: \: \: \rightarrow a2-b2 = (a+b)(a-b)\\ \frac{(2x-3y)(2x+3y)}{(2x+3y)(4x-9y)} = \frac{2x-3y}{4x-9y}\]
6) \[\frac{4x^2-13x+3}{4x-1} =?\]
Explanation:\[\frac{(x-3)(4x-1)}{4x-1} =x-3\]
7) \[\frac{(x+3)(x^2+8x+15)}{(x-2)(x^2+6x+9)} = ?\]
Explanation: \[\frac{(x+3)(x+3)(x+5)}{(x-2)(x+3)(x+3)} = \frac{x+5}{x-2}\]
8) \[\frac{(x+y)}{x-y}\times \frac{x+y}{x-y} = ?\]
Explanation: \[\frac{(x+y)^2}{(x-y)^2}\]
9) \[\frac{x^2-y^2}{x-y} \times \frac{x}{x+y} =?\]
Explanation: \[\frac{(x-y)(x+y)}{x-y}\times \frac{x}{x+y}= x\]
10) \[\frac{6x^2 y^3 z}{6z^2 } \times \frac{10z^2}{12xy^2 }\]
Explanation: \[\frac{2\times 3\times x\times x\times y\times y\times y\times 2\times 5\times z\times z}{2\times 3\times z\times z\times 2\times 2\times 3\times x\times y\times y} = \frac{5xyz}{6}\]