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a) 5x - 15y = 5(x - 3y)
b) \(\dfrac{3}{5}\)x2 + 5x4 - x2 - y
= \(\dfrac{3}{5}\)x2 + 5x2.x2 - x2 - y
= x2(\(\dfrac{3}{5}\) + 5x2 -1) - y
c) 14x2y2 - 21xy2 + 28x2y
= 7xy.xy - 7xy.3y + 7xy.4x
= 7xy(xy - 3y + 4x)
= 7xy[(xy - 3y) + 4x]
= 7xy[y(x - 3) +4x]
d) \(\dfrac{2}{7}x\)(3y - 1) - \(\dfrac{2}{7}y\)(3y - 1)
= (3y - 1).(\(\dfrac{2}{7}x\) - \(\dfrac{2}{7}y\) )
= (3y - 1).[\(\dfrac{2}{7}\)(x - y)]
e) x3 - 3x2 + 3x - 1
= x2.x - 3x.x + 3.x - 1
= x(x2-3x+3) - 1
g) 27x3 + \(\dfrac{1}{8}\)
= (3x)3 + \(\left(\dfrac{1}{2}\right)^3\)
= (3x + \(\dfrac{1}{2}\)).(9x2 - \(\dfrac{3}{2}\)x + \(\dfrac{1}{4}\))
h) (x+y)3 - (x-y)3
= 2(3x2y) + 2y3
f) (x+y)2 - 4x2
= -3x2 + y(2x + y)
a)(2m-7)^2=(2m)^2-2.2m.7+7^2= 4m^2-28m+49
b)(3m-1)^3=(3m)^3-1^3-3.3m.1(3m-1)=9m^3-1- 27m^2-9m
c)(5x+12)^2=(5x)^2+2.5x.12+12^2=25x^2+120x+144
d)(3-z^2)^2=3^2- 2.3.z^2+(z^2)^2=9-6z^2+z^4
e)(4a+7b)^3=(4a)^3+(7b)^3+3.4a.7b(4a+7b)=64a^3+343b^3+336a^2b+588ab^2
f)(x+y^2)^2=x^2+2x.y^2+(y^2)^2=x^2+2xy^2+y^4
g)(2x-z)^3=(2x)^3-z^3-3.2x.z(2x-z)=8x^3-z^3-12x^2z+6xz^2
h)(3y+1/2)^3=(3y)^3+(1/2)^3+3.3y.1/2(3y+1/2)=27.y^3+1/8+27/2.y^2+9/4.y
\(=8x^{3-2m}\cdot y^{6-3n}\cdot3x^{2m-1}-8x^{3-2m}\cdot y^{6-3n}\cdot\dfrac{3}{7}y^{3n-5}+8x^{3-2m}\cdot y^{6-3n}\cdot x^{2m}y^{3n}-8x^{3-2m}\cdot y^{6-3n}\cdot3y^2\)
\(=24x^2y^{6-3n}-\dfrac{24}{7}x^{3-2m}\cdot y+8x^3y^6-24x^{3-2m}\cdot y^{8-3n}\)