Find the square. (1/4A + 1/4B)^2

a) 1/16A^2 + 1/8AB + 1/16B^2
b) 1/4A^2 + 1/8AB + 1/4B^2

Question

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Respuesta :

mathstudent55 mathstudent55 · Answer 1 · 2018-09-26T21:08:55+02:00

[tex] (a + b)^2 = a^2 + 2ab + b^2 [/tex]

[tex] (\dfrac{1}{4}A + \dfrac{1}{4}B)^2 = [/tex]

[tex] = \dfrac{1}{16}A^2 + \dfrac{1}{8}AB + \dfrac{1}{16}B^2 [/tex]

Answer: A.

Another way to solve by factoring 1/4.

[tex] (\dfrac{1}{4}A + \dfrac{1}{4}B)^2 = [/tex]

[tex] = [\dfrac{1}{4}(A + B)]^2 [/tex]

[tex] = (\dfrac{1}{4})^2(A + B)^2 [/tex]

[tex] = \dfrac{1}{16}(A^2 + 2AB + B^2) [/tex]

[tex] = \dfrac{1}{16}A^2 + \dfrac{1}{16}2AB + \dfrac{1}{16}B)^2 [/tex]

[tex] = \dfrac{1}{16}A^2 + \dfrac{1}{8}AB + \dfrac{1}{16}B)^2 [/tex]

jimrgrant1 jimrgrant1 · Answer 2 · 2018-09-26T21:12:27+02:00

[tex]\frac{1}{16}[/tex] A² + [tex]\frac{1}{8}[/tex] AB + [tex]\frac{1}{16}[/tex] B²

([tex]\frac{1}{4}[/tex] A + [tex]\frac{1}{4}[/tex] B )²

= ([tex]\frac{1}{4}[/tex] A + [tex]\frac{1}{4}[/tex] B )([tex]\frac{1}{4}[/tex] A + [tex]\frac{1}{4}[/tex] B )

expand the factors using FOIL

= ([tex]\frac{1}{4}[/tex] A )² + (2 × [tex]\frac{1}{16}[/tex] AB + ([tex]\frac{1}{4}[/tex] B )²

= [tex]\frac{1}{16}[/tex] A² + [tex]\frac{1}{8}[/tex] AB + [tex]\frac{1}{16}[/tex] B²