Simplification
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Algebraic formulas:
- (a+b)2 = a2 + b2 + 2ab
- (a-b)2 = a2 + b2 – 2ab
- (a+b) (a-b) = a2 – b2
- (a + b)3 = a3 + b3 + 3ab(a + b)
- (a – b)3 = a3 – b3 – 3ab(a – b)
- a3 + b3 + c3 – 3abc = (a + b + c)(a2 + b2 + c2 – ab – bc -ac)
- a2 + b2 =½ [(a + b)2 + (a – b)2]
- (a + a) (a + b) (a + c) = a3 + (a + b +c)a2 + (ab + bc + ca)a + abc
- a3 + b3= (a + b) (a2 – ab + b2)
- a3 – b3 = (a – b) (a2 + ab + b2)
- a2 + b2 + c2 -ab – bc – ca = ½ [(a-b)2 + (b-c)2 + (c-a)2]
2 Simplify : $$\frac{{\frac{5}{3} \times \frac{7}{{51}}{\text{ of }}\frac{17}{5} - \frac{1}{3}}}{{\frac{2}{9} \times \frac{5}{7}{\text{ of }}\frac{{28}}{5} - \frac{2}{3}}}\ \ = ?$$
A
$$\frac{1}{3}$$
B
$$\frac{1}{6}$$
C
4
D
2
5 Simplify : $$1 - \left[ {1 - \left\{ {1 - \left( {1 - \overline {1 - 1} } \right)} \right\}} \right]$$
A
0
B
1
C
2
D
3
6 Simplify : $${{{5 \over 3} \times {7 \over {51}}{\text{ of }}{{17} \over 5} - {1 \over 3}} \over {{2 \over 9} \times {5 \over 7}{\text{ of }}{{28} \over 5} - {2 \over 3}}}$$
A
$$\frac{1}{2}$$
B
4
C
2
D
$$\frac{1}{4}$$
