\displaystyle \textbf{Question 1: }\text{Factorize }6xy-4xz.
\displaystyle \text{Answer:}
\displaystyle 6xy-4xz=2x(3y-2z).
\displaystyle \\

\displaystyle \textbf{Question 2: }\text{Factorize }9bx^2+15b^2x.
\displaystyle \text{Answer:}
\displaystyle 9bx^2+15b^2x=3bx(3x+5b).
\displaystyle \\

\displaystyle \textbf{Question 3: }\text{Factorize }4a^2b-6ab^2+8ab.
\displaystyle \text{Answer:}
\displaystyle 4a^2b-6ab^2+8ab=2ab(2a-3b+4).
\displaystyle \\

\displaystyle \textbf{Question 4: }\text{Factorize }5x^2+15x^3-20x.
\displaystyle \text{Answer:}
\displaystyle 5x^2+15x^3-20x=5x(x+3x^2-4).
\displaystyle =5x(3x^2+x-4).
\displaystyle \\

\displaystyle \textbf{Question 5: }\text{Factorize }2x^3+x^2-4x.
\displaystyle \text{Answer:}
\displaystyle 2x^3+x^2-4x=x(2x^2+x-4).
\displaystyle \\

\displaystyle \textbf{Question 6: }\text{Factorize }a^3b-a^2b^2-b^3.
\displaystyle \text{Answer:}
\displaystyle a^3b-a^2b^2-b^3=b(a^3-a^2b-b^2).
\displaystyle \\

\displaystyle \textbf{Question 7: }\text{Factorize } 28a^2b^2c-42ab^2c^2.
\displaystyle \text{Answer:}
\displaystyle 28a^2b^2c-42ab^2c^2 =14ab^2c(2a-3c).
\displaystyle \\

\displaystyle \textbf{Question 8: }\text{Factorize } 15x^2y-6xy^2+9y^3.
\displaystyle \text{Answer:}
\displaystyle 15x^2y-6xy^2+9y^3 =3y(5x^2-2xy+3y^2).
\displaystyle \\

\displaystyle \textbf{Question 9: }\text{Factorize } 10x^2y+15xy^2-25x^2y^2.
\displaystyle \text{Answer:}
\displaystyle 10x^2y+15xy^2-25x^2y^2 =5xy(2x+3y-5xy).
\displaystyle \\

\displaystyle \textbf{Question 10: }\text{Factorize }18x^2y-24xyz.
\displaystyle \text{Answer:}
\displaystyle 18x^2y-24xyz=6xy(3x-4z).
\displaystyle \\

\displaystyle \textbf{Question 11: }\text{Factorize } 27a^3b^3-45a^4b^2.
\displaystyle \text{Answer:}
\displaystyle 27a^3b^3-45a^4b^2 =9a^3b^2(3b-5a).
\displaystyle \\

\displaystyle \textbf{Question 12: }\text{Factorize } 4(a+b)-6(a+b)^2.
\displaystyle \text{Answer:}
\displaystyle 4(a+b)-6(a+b)^2
\displaystyle =2(a+b)\{2-3(a+b)\}
\displaystyle =2(a+b)(2-3a-3b).
\displaystyle \\

\displaystyle \textbf{Question 13: }\text{Factorize } 2a(3x+5y)-5b(3x+5y).
\displaystyle \text{Answer:}
\displaystyle 2a(3x+5y)-5b(3x+5y)
\displaystyle =(3x+5y)(2a-5b).
\displaystyle \\

\displaystyle \textbf{Question 14: }\text{Factorize } 2x(p^2+q^2)+4y(p^2+q^2).
\displaystyle \text{Answer:}
\displaystyle 2x(p^2+q^2)+4y(p^2+q^2)
\displaystyle =2(p^2+q^2)(x+2y).
\displaystyle \\

\displaystyle \textbf{Question 15: }\text{Factorize } 8(3a-2b)^2-10(3a-2b).
\displaystyle \text{Answer:}
\displaystyle 8(3a-2b)^2-10(3a-2b)
\displaystyle =2(3a-2b)\{4(3a-2b)-5\}
\displaystyle =2(3a-2b)(12a-8b-5).
\displaystyle \\

\displaystyle \textbf{Question 16: }\text{Factorize } x(x+y)^3-3x^2y(x+y).
\displaystyle \text{Answer:}
\displaystyle x(x+y)^3-3x^2y(x+y)
\displaystyle =x(x+y)\{(x+y)^2-3xy\}
\displaystyle =x(x+y)(x^2+2xy+y^2-3xy)
\displaystyle =x(x+y)(x^2-xy+y^2).
\displaystyle \\

\displaystyle \textbf{Question 17: }\text{Factorize } a(3x-2y)+b(2y-3x).
\displaystyle \text{Answer:}
\displaystyle 2y-3x=-(3x-2y).
\displaystyle \therefore a(3x-2y)+b(2y-3x)
\displaystyle =a(3x-2y)-b(3x-2y)
\displaystyle =(3x-2y)(a-b).
\displaystyle \\

\displaystyle \textbf{Question 18: }\text{Factorize } a(b-c)^2-d(c-b).
\displaystyle \text{Answer:}
\displaystyle c-b=-(b-c).
\displaystyle \therefore a(b-c)^2-d(c-b)
\displaystyle =a(b-c)^2+d(b-c)
\displaystyle =(b-c)\{a(b-c)+d\}.
\displaystyle \\

\displaystyle \textbf{Question 19: }\text{Factorize } a(4a-b)+2b(4a-b)-c(4a-b).
\displaystyle \text{Answer:}
\displaystyle a(4a-b)+2b(4a-b)-c(4a-b)
\displaystyle =(4a-b)(a+2b-c).
\displaystyle \\

\displaystyle \textbf{Question 20: }\text{Factorize } m(mx+ny)^2+mn(mx+ny)+n(mx+ny).
\displaystyle \text{Answer:}
\displaystyle m(mx+ny)^2+mn(mx+ny)+n(mx+ny)
\displaystyle =(mx+ny)\{m(mx+ny)+mn+n\}
\displaystyle =(mx+ny)(m^2x+mny+mn+n).
\displaystyle \\

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