How do you multiply (4x-√3)(4x+√3)?

Question

Genesis Allen · Accepted Answer

#16x^2 -3# #(4x-sqrt3)(4x+sqrt3)# Use FOIL - firsts, outers, inners, lasts first: #4x*4x = 16x^2# outer: #4x*sqrt3 = 4sqrt3x# inner: #-sqrt3*4x = -4sqrt3x# lasts : #-sqrt3*sqrt3 = -3# Then add all the results #16x^2+4sqrt3 -4sqrt3 -3# The #4sqrt3 and -4sqrt3# cancel each other out so you are left with #16x^2 -3#

Ethan Adkins · Answer

#color(green)(16x^2-3# #(4x-sqrt3)(4x+sqrt3)# #color(white)(aaaaaaaaaaaaa)##4x-sqrt3# #color(white)(aaaaaaaaaaa)## xx underline(4x+sqrt3)# #color(white)(aaaaaaaaaaaaa)##16x^2-4xsqrt3# #color(white)(aaaaaaaaaaaaaaaaaa)##ul(+4xsqrt3-3)# #color(white)(aaaaaaaaaaaaa)##16x^2##color(white)(aaaaaaaa)-3# #color(white)(aaaaaaaaaaaaa)##color(green)(16x^2-3#

Eva Abramson · Answer

An alternative approach is the well-known F.O.I.L. method, which has the drawback of only being able to work with the product of two binomials.

Given: #(4x-sqrt3)(4x+sqrt3) = ?#

Step 1: Extend the initial terms:

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

Step 2: Extend the external terms by:

#(4x)(sqrt3) = 4sqrt3x#

Step 3: Increase the inside terms by one.

#(4x)(-sqrt3) = -4sqrt3x#

Step 4: Increase the final terms by:

#-sqrt3sqrt3= -3#

Step 5: Add all terms (note that this is a unique instance where the total of the outside and inside terms is zero):

#16x^2 color(red)(cancel(+ 4sqrt3x-4sqrt3x)) - 3 = 16x^2-3#

Because the distributive method can handle polynomials of any size, that's why I like it.

Given: #(4x-sqrt3)(4x+sqrt3) = ?#

Step 1: Divide the second factor among the first factor's terms:

#4x(4x+sqrt3)-sqrt3(4x+sqrt3)#

Note that the number of terms in either factor can be used in the aforementioned step, and it makes no difference which factor you distribute.

Step 2. Use the distributive property #a(b+c) = ab + ac# to eliminate the parenthesis:

#16x^2+4sqrt3x-4sqrt3x-sqrt3sqrt3#

Please note that the terms we obtained using the F.O.I.L. method are the same as ours.

Step 3: Merge similar terms together:

#16x^2-3#

Eli Assouline · Answer

undefined To multiply (4x-√3)(4x+√3), you can use the distributive property and the difference of squares formula. First, multiply the terms together:

(4x)(4x) = 16x^2
(4x)(√3) = 4x√3
(-√3)(4x) = -4x√3
(-√3)(√3) = -3

Combine like terms:

16x^2 - 3

So, the result of multiplying (4x-√3)(4x+√3) is 16x^2 - 3.