How do you multiply #(4z + \frac { 1} { 2} ) ^ { 2}# using the rule for the square of a binomial?

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Answer 1 · 2017-04-05T20:09:07

#16z^2+4z+1/4#

Recall,

#a^2=a*a#

So,

#(4z+1/2)^2=(4z+1/2)*(4z+1/2)#

Binomial expansion,

#16z^2+2z+2z+1/4#

Collect like terms,

#16z^2+4z+1/4#

Factor (if needed),

#4(4z^2+z+1/16)#

Answer 2 · 2017-04-05T20:15:42

#16z^2 +4z+1/4#

The rule for squaring a binomial is a 5-step process:

square the first term

multiply the signs

multiply the two terms and double

PLUS

square the last term

#(x+-y)^2 = x^2 +-2xy +y^2#

#(4z+1/2)^2 = 16z^2 +4z+1/4#

Applying the 5 steps:

#(4z)^2 = 16z^2#

#+ xx + = +#

#4z xx 1/2 xx2 = 2z xx 2 = 4z#

#+#

#(1/2)^2 = 1/4#