1) $(2x+3)^2=(2x)^2+2.2x.3+9=4x^2+12x+9$
2) $(3x+2y)^2=(3x)^2+2.3x.2y+(2y)^2=9x^2+12xy+4y^2$
3) $(x+3y)^2=x^2+2.x.3y+(3y)^2=x^2+6xy+9y^2$
4) $(5x+1)^2=(5x)^2+2.5x.1+1=25x^2+10x+1$
5) $(4x+2y)^2=(4x)^2+2.4x.2y+(2y)^2=16x^2+16xy+4y^2$
6) $(5x+y)^2=(5x)^2+2.5x.y+y^2=25x^2+10xy+y^2$
7) $(1+5y)^2=1+2.1.5y+(5y)^2=1+10y+25y^2$
8) $(a+b+c)^2=[(a+b)+c]^2=(a+b)^2+2.(a+b).c+c^2=a^2+2ab+b^2+2ac+2bc+c^2=a^2+b^2+c^2+2ab+2bc+2ac$
9) $(x+y+z)^2=[(x+y)+z]^2=(x+y)^2+2.(x+y).z+z^2=x^2+2xy+y^2+2xz+2yz+z^2=x^2+y^2+z^2+2xy+2yz+2xz$
10) $(3a-1)^2=(3a)^2-2.3a.1+1=9a^2-6a+1$
11) $(a-2)^2=a^2-2.a.2+4=a^2-4a+4$
12) $(1-5a)^2=1-2.1.5a+(5a)^2=1-10a+25a^2$
13) $(3a-2b)^2=(3a)^2-2.3a.2b+(2b)^2=9a^2-12ab+4b^2$
14) $(4-3a)^2=4^2-2.4.3a+(3a)^2=16-24a+9a^2$
15) $(5a-4b)^2=(5a)^2-2.5a.4b+(4b)^2=25a^2-40ab+16b^2$
16) $[(a+b)-c]^2=(a+b)^2-2.(a+b).c+c^2=a^2+2ab+b^2-2ac-2bc+c^2=a^2+b^2+c^2+2ab-2bc-2ac$
17) $(a-b+c)^2=[(a-b)+c]^2=(a-b)^2+2.(a-b).c+c^2=a^2-2ab+b^2+2ac-2bc+c^2=a^2+b^2+c^2-2ab-2bc+2ac$
18) $(a-b-c)^2=[(a-b)-c]^2=(a-b)^2-2.(a-b).c+c^2=a^2-2ab+b^2-2ac+2bc+c^2=a^2+b^2+c^2-2ab+2bc-2ac$
19) $\Bigg(\dfrac{1}{2}x-1\Bigg)\Bigg(\dfrac{1}{2}x+1\Bigg)=\Bigg(\dfrac{1}{2}x\Bigg)^2-1^2=\dfrac{1}{4}x^2-1$
20) $\Bigg(\dfrac{3}{4}x+2\Bigg)\Bigg(\dfrac{3}{4}x-2\Bigg)=\Bigg(\dfrac{3}{4}x\Bigg)^2-2^2=\dfrac{9}{16}x^2-4$
21) $\Bigg(5x-\dfrac{3}{2}\Bigg)\Bigg(5x+\dfrac{3}{2}\Bigg)=(5x)^2-\Bigg(\dfrac{3}{2}\Bigg)^2=25x^2-\dfrac{9}{4}$
22) $(2a^2-7)(2a^2+7)=(2a^2)^2-7^2=4a^4-49$
23) $(x+y+z)(x+y-z)=[(x+y)+z][(x+y)-z]=(x+y)^2-z^2$
