Multiply the binomials: (3/4 a^2+3b^2) and (a^2-2/3b^2)
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= (\frac{3}{4a2} + 3b2 )4( \frac{a2 - 2}{3b2} )=(
4a2
3
+3b2)4(
3b2
a2−2
)
=( \frac{3}{8a} + 6b) \: \times 2 \times \frac{2a - 2}{3b}=(
8a
3
+6b)×2×
3b
2a−2
= \frac{3 + 48ab}{8a} \times 2 \times \frac{2a - 2}{3b}=
8a
3+48ab
×2×
3b
2a−2
= \frac{3 + 48ab}{8a} \times 2 \times \frac{2a - 1}{3b}=
8a
3+48ab
×2×
3b
2a−1
= \frac{3 + 48ab}{4a} \times \frac{2(a - 1)}{3b}=
4a
3+48ab
×
3b
2(a−1)
= \frac{3(1 + 16ab)}{2a} \times \frac{a - 1}{3b}=
2a
3(1+16ab)
×
3b
a−1
= \frac{(1 + 16ab) \times (a - 1)}{2ab}=
2ab
(1+16ab)×(a−1)
= \frac{a - 1 + 16a {}^{2} b - 16ab}{2ab}=
2ab
a−1+16a
2
b−16ab
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