How do you expand #(5x+2y)^3#?

1 Answer
Dec 21, 2017

#(5x+2y)^3=125x^3+150x^2y+60xy^2+8y^3#

Explanation:

We can look at the fourth row (we're counting from zero) of Pascal's triangel to obtain the coefficients of the expansion:
#color(white)(aaaaaaaaaaaaaaaaaaa)1#
#color(white)(aaaaaaaaaaaaaaaaa)1color(white)(aaa)1#
#color(white)(aaaaaaaaaaaaaaa)1color(white)(aaa)2color(white)(aaa)1#
#color(white)(aaaaaaaaaaaaa)1color(white)(aaa)3color(white)(aaa)3color(white)(aaa)1#

Knowing that the exponents of the left term decrease and the exponents of the right increase, we get:
#(5x+2y)^3=(5x)^3+3(5x)^2(2y)+3(5x)(2y)^2+(2y)^3#

#=125x^3+3*25x^2*2y+3*5x*4y^2+8y^3#

#=125x^3+150x^2y+60xy^2+8y^3#