Question

Expand  (x+3y +5z)2  using suitable identity​

Answer 1

Answer:

2x + 6y + 10 z

Step-by-step explanation:

2(x+3y+5z) _ 2x+6y+10z

Answer 2

Answer:

$(x+3y +5z)^2 = x^2 + 9y^2 + 25z^2 + 6xy +45yz) +10xz$

Step-by-step explanation:

$(a + b + c)^2 = (a + x)^2 = a^2 + 2ax + x^2$

$= a^2 + 2a (b + c) + (b + c)^2$

 $= a^2 + 2ab + 2ac + (b^2 + c^2 + 2bc)$

$= a^2 + b^2 + c^2 + 2ab + 2bc + 2ca$

Therefore, $(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca$

Given: $(x+3y +5z)^2$

a = x, b = 3y and c = 5z

$(x + 3y + 5z)^2 = x^2 + (3y)^2 + (5z)^2 + 2(x)(3y) + 2(3y)(5z) + 2(5z)(x)$

$= x^2 + 9y^2 + 25z^2 + 6xy +9y(5z) +10xz$

$= x^2 + 9y^2 + 25z^2 + 6xy +45yz) +10xz$