Question 1: Multiply:

  1.  {8x}^2\times{}\left(-5x\right)=-40x^3  
  2.  \frac{2}{3}ab\times{}\left(-6a^2b\right)=-{4a}^3b^2   
  3.  {7x}^2y^3\times{}\left(-4x^3y\right)=-28x^5y^4  
  4.   (\frac{-5}{9}{ax}^2)\times{}\left(\frac{-3}{5}{bxa}^2\right)=\frac{1}{3}\ x^3\ a^3\ b  
  5.  \left(\frac{-2}{3}a^6b^5\right)\times{}\left(\frac{-9}{4}a^3b^3\right)=\frac{3}{2}a^9b^8 
  6.   \ (\frac{-5}{8}p^2q)\times{}(\frac{16}{25}{pq}^2)=\frac{-2}{5}p^3q^3 

 

Question 2: Multiply:

i)  \left(2x^2-5x+6\right)\times{}\left(-3x\right)  

 =-6x^3+15x^2-18x    

ii)  \left(3-2y-y^2\right)\times{}\left(-4xy\right)  

 =-12xy+8{xy}^2+{4xy}^3    

iii)  \left({3x}^2y-2xy^2+5xy-6\right)\times{}4xy  

 ={12x}^3y^2-{8x}^2y^3+20x^2y^2-24xy    

iv)  \left(7a^3-5ab^2-{2b}^3+3ab+2a-5\right)\times{}\left(-3{ab}^2\right) 

 =  b^2+15\ a^2b^4+{6ab}^5-9\ a^2b^3-{6a}^2b^2+{15ab}^2    

 

Question 3: Multiply:

i)  \left(a+5\right)\left(a+4\right)=a^2+9a+20    

ii)  \left(x-3\right)\left(x+8\right)=x^2-3x+8x-24    

 =x^2+5x-24    

iii)  \left(y-4\right)\left(y-6\right)=y^2-4y-6y+24    

 =y^2+10y+24    

iv)  \left(z+1\right)\left(z-7\right)=\ z^2+z-7z-7    

 =z^2-6z-7    

v)  \left(3a-2b\right)\left(2a+3b\right)={6a}^2-4ab+9ab-{6b}^2   

 ={6a}^2+5ab-{6b}^2    

vi)  \left(5x+4y\right)\left(2x-3y\right)={10x}^2+8xy-15xy-12y^2   

 =10x^2-7xy-12y^2    

 

Question 4: Multiply:

i)  (4x^2+3x-5)\times{}(2x+3)   

 =8x^3+{6x}^2-10x+{12x}^2+9x-15   

 ={8x}^3+{18x}^2-x-15   

ii)  (3-2x+5x^2)\times{}(5x-4)   

 =15x-10x^2+25x^3-12+8x-20x^2   

 =25x^3-30x^2+23x-12   

iii)  \left(x^3-5x+3\right)\left(2x+9\right)   

 ={2x}^4-{10x}^2+6x+{9x}^3-45x+27   

 =2x^4+{9x}^3-10x^2-39x+27   

iv)  \left(4x^2+xy+{9y}^2\right)\times{}\left(2x-3y\right)   

 ={8x}^3+{2x}^2y+18{xy}^2-12x^2y-{6xy}^2-27y^3   

 ={8x}^3-27y^3-10x^2y+12{xy}^2   

 

Question 5: Multiply:

i)  \left({4x}^2-4x+1\right)\times{}({2x}^2+x-2)   

 ={8x}^4-{8x}^3+{2x}^2+{4x}^3-{4x}^2+x-{8x}^2+8x-2   

 ={8x}^4-{4x}^3-{10x}^2+9x-2   

ii)  \left({3x}^2+4x-5\right)\times{}\left({4x}^2-7x+2\right)   

 =12x^4+{16x}^3-20x^2-{21x}^3-{28x}^2+35x+{6x}^2+8x-10   

 =12x^4-5x^3-42x^2+43x-10   

iii)  \left({4x}^2+24xy+{3y}^2\right)\left(x^2-xy+y^2\right)   

 ={4x}^4+{24x}^3y+{3x}^2y^2-{4x}^3y-24x^2y^2-3xy^3 \\ +4x^2y^2+24xy^3+4y^4   

 ={4x}^4+{20x}^3y-{17x}^2y^2+{21xy}^3+3y^4   

iv)  \left({6x}^3-{5x}^2+4x+1\right)\times{}\left(x^2+7x-1\right)   

 =6x^5-{5x}^4+{4x}^3+x^2+{42x}^4-35x^3+28x^2+7x-6x^3 \\ +5x^2-4x-1+3x-1   

 =6x^5+37x^4-37x^3+34x^2+3x-1   

v)  \left(8x^4-{3x}^2+9x-8\right)\times{}\left(2x^2-5x+3\right)   

 =16x^6-{6x}^4+{18x}^3-{16x}^2-40x^5 \\ +{15x}^3-45x^2+40x+{24x}^4-{9x}^2+27x-24   

 =16x^6-{40x}^5+18x^4+33x^3-70x^2+67x-24   

vi)  \left(3x^5-{7x}^3+2x^2-x+4\right)\times{}\left(x^3-{2x}^2+3x-1\right)   

 ={3x}^8-7x^6+{2x}^5-x^4+{4x}^3+14x^5-4x^4 \\ +{2x}^3-6x^7-8x^2+9x^6-21x^4+{6x}^3-{3x}^2\\ +12x-3x^5 +{7x}^3-{2x}^2+x-4   

 =3x^8+2x^6+13x^5-{26x}^4+{19x}^3-{6x}^7+{13x}^2+13x-4   

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