Use suitable identities to find the following products.1) (2x +7y) (2x+7y). 2) (3x-5y) (3x-5y). 3) (5x+3y) (5x-3y). 4) (5x+2y) (5x+3y)
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1) (2x+7y)(2x+7y)=(2x+7y)^2
since (a+b)^2=a^2+b^2+2ab
=(2x)^2+(7y)^2 +2*2x*7y
=4x^2+49y^2+28xy
2)(3x-5y)(3x-5y)=(3x-5y)^2
a^2+b^2-2ab=(a-b)^2
= (3x)^2+(5y)^2-2*3x*5y
=9x^2+25y^2-30xy
3)(5x+3y)(5x-3y)
since (a+b)(a-b)=a^2-b^2
= (5x)^2-(3y)^2
= 25x^2-9y^2
4)(5x+2y)(5x+3y)
multiplying the two brackets
=(5x)^2+5x*3y+2y*5x+3y*2y
=25x^2+15xy+10xy+6y^2
since (a+b)^2=a^2+b^2+2ab
=(2x)^2+(7y)^2 +2*2x*7y
=4x^2+49y^2+28xy
2)(3x-5y)(3x-5y)=(3x-5y)^2
a^2+b^2-2ab=(a-b)^2
= (3x)^2+(5y)^2-2*3x*5y
=9x^2+25y^2-30xy
3)(5x+3y)(5x-3y)
since (a+b)(a-b)=a^2-b^2
= (5x)^2-(3y)^2
= 25x^2-9y^2
4)(5x+2y)(5x+3y)
multiplying the two brackets
=(5x)^2+5x*3y+2y*5x+3y*2y
=25x^2+15xy+10xy+6y^2
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