Question

expand the following
i)(3x+5y)^2
ii)(√2x+3y)^2​

Answer 1

Step-by-step explanation:

WE CAN DO BOTH BY (a+b)²=a²+b²+2ab

1) (3x+5y)²

=(3x)²+(5y)²+2(3x)(5y)

=9x²+25y²+30xy

2) (√2x+3y)²

=(√2x)²+(3y)²+2(√2x)(3y)

=2x²+9y²+6√2xy

Answer 2

Answer:

i) 9$x^{2}$ + 30xy + $25y^{2}$

ii) 2$x^{2}$ + 6$\sqrt{2}$ xy + 9$y^{2}$

Step-by-step explanation:

Use the identity : $(a+b)^{2} = a^{2} + 2ab + b^{2}$

i) (3x+5y)^2 =  

$(3x)^{2} + 2(3x)(5y) + (5y)^{2} \\ =9x^{2} + 30xy + 25y^{2}$

ii)(√2x+3y)^2​ =

$(\sqrt{2}x) ^{2} + 2(\sqrt{2}x)(3y) + (3y)^{2} \\= 2x^{2} + 6\sqrt{2}xy + 9y^{2}$