How do you expand #(4x-3)^2#?

3 Answers
Nam D.
May 29, 2018

#16x^2-24x+9#

Explanation:

Given: #(4x-3)^2#

Use the binomial theorem for the second power, which we find that:

  • #(a+b)^2=a^2+2ab+b^2#

  • #(a-b)^2=a^2-2ab+b^2#

Here #a=4x,b=3#, and we use the second formula.

So, we get:

#(4x-3)^2=(4x)^2-2*3*4x+3^2#

#=16x^2-24x+9#

Calvin
May 29, 2018

#16x^2 - 24x +9#

Explanation:

First let

#a = 4x#

#b = -3#

we use the formula

#a^2 + 2ab + b^2#

so
#(4x)^2 + 2(4x)(-3) + (-3)^2#

the result will be

#16x^2 - 24x + 9#

Tony B
May 29, 2018

#16x^2-24x+9#

Explanation:

Given: #(4x-3)^2#

Write as: #color(blue)((4x-3))color(green)( (4x-3) )#

Multiply everything in the second bracket by everything in the first.

#color(green)(color(blue)(4x)(4x-3)color(white)("ddd")color(blue)(-3)(4x-3)) larr# notice the way the minus
#color(white)("dddddddddddddddddddddddd")#followed the #color(blue)(3)#

#16x^2ubrace(-12xcolor(white)("ddd") -12x)+9#

#16x^2color(white)("dddd")-24xcolor(white)("dddd")+9#

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