This is called finding the Square of a Binomial.
#rarr# An expression with 2 terms is being squared, which means "being multiplied by itself"
While it is perfectly fine to write out the two brackets and multiply them that way, there is a short cut rule which is VERY useful to know!
This skill pops up all the time in Algebra and you will save a good deal of time if you can just write down the answer immediately.
This also forms the basis for a process called :
"Completing the square"
Rule for Squaring a Binomial #rarr# a trinomial
#color(red)("1. Square the first term in the bracket")#
#color(blue)("2. Multiply the two signs in the bracket")#
#color(magenta)("3. Multiply the two terms and double the product")#
#color(olive)("4. PLUS +")#
#color(lime)("5. Square the second term in the bracket")#
#(5x^5-y^4)^2 = (5x^5-y^4) xx(5x^5-y^4)#
= # color(red)(25x^10) color(blue)(-)color(magenta)(10x^5y^4) color(olive)(+) color(lime)(y^8)#
Here are some more examples:
#(3x^3 -4y)^2 = 9x^6-24x^3y+16y^2#
#(7p-5q)^2 = 49p^2 -70pq +25q^2#
#3(2m^2 -3n)^2#
=# 3(4m^4-12m^2n+9n^2)#
=#12m^4-36m^2n+27n^2#
