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elena-s [515]
3 years ago
14

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

Mathematics
2 answers:
alisha [4.7K]3 years ago
6 0

(a + b)^2 = a^2 + 2ab + b^2

(\dfrac{1}{4}A + \dfrac{1}{4}B)^2 =

= \dfrac{1}{16}A^2 + \dfrac{1}{8}AB + \dfrac{1}{16}B^2

Answer: A.

Another way to solve by factoring 1/4.

(\dfrac{1}{4}A + \dfrac{1}{4}B)^2 =

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

= (\dfrac{1}{4})^2(A + B)^2

= \dfrac{1}{16}(A^2 + 2AB + B^2)

= \dfrac{1}{16}A^2 + \dfrac{1}{16}2AB + \dfrac{1}{16}B)^2

= \dfrac{1}{16}A^2 + \dfrac{1}{8}AB + \dfrac{1}{16}B)^2

BabaBlast [244]3 years ago
6 0

\frac{1}{16} A² + \frac{1}{8} AB + \frac{1}{16} B²

(\frac{1}{4} A + \frac{1}{4} B )²

= (\frac{1}{4} A + \frac{1}{4} B )(\frac{1}{4} A + \frac{1}{4} B )

expand the factors using FOIL

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

= \frac{1}{16} A² + \frac{1}{8} AB + \frac{1}{16} B²


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