Topics

1). If $$\Large a^{2}+b^{2}=24,\ ab=4$$ find the value of $$\Large \left(a-b\right)$$
 A). 4 B). 6 C). 3 D). 2
2). If $$\Large x^{2}+\frac{1}{x^{2}}=38,$$ find the value of $$\Large x-\frac{1}{x}$$
 A). 8 B). 6 C). 4 D). 2
3). Simpllify: $$\Large \frac{a^{3}-b^{3}}{a^{2}+ab+b^{2}}$$
 A). $$\Large \left(a + b\right)$$ B). $$\Large \left(a - b\right)^{2}$$ C). $$\Large \left(a - b\right)$$ D). $$\Large \left(a + b\right)^{2}$$
4). Find the factors of $$\Large x^{2}+10x+24$$
 A). $$\Large \left(x-6\right) \left(x-4\right)$$ B). $$\Large \left(x-6\right) \left(x+4\right)$$ C). $$\Large \left(x+6\right) \left(x-4\right)$$ D). $$\Large \left(x+6\right) \left(x+4\right)$$
5). Simplify $$\Large \frac{ \left(a^{3}+b^{3}\right) \left(a^{2}-b^{2}\right) }{ \left(a^{2}-ab+b^{2}\right) \left(a-b\right) }$$
 A). $$\Large \left(a+b\right)^{2}$$ B). $$\Large \left(a-b\right)^{2}$$ C). $$\Large \left(a+b\right) \left(a-b\right)$$ D). None of these

6). Find the common factor of $$\Large x^{2}+\frac{1}{x^{2}}=102$$, then the value of $$\Large \left(x-\frac{1}{x}\right)$$ is
 A). 10 B). 12 C). 6 D). 4
7). Factorise: $$\Large x^{2}+18x+81$$
 A). $$\Large \left(x+9\right) \left(x-9\right)$$ B). $$\Large \left(x+9\right)^{2}$$ C). $$\Large \left(x+3\right)^{2}$$ D). $$\Large \left(x-9\right)^{2}$$
8). Simplify $$\Large \frac{ \left(x^{2}-4\right) \left(x^{3}-8\right) }{ \left(x-2\right)^{2} \left(x^{2}+2x+4\right) }=?$$
 A). $$\Large \left(x-2\right)^{2}$$ B). $$\Large \left(x+2\right)^{2}$$ C). $$\Large \left(x+2\right)$$ D). $$\Large \left(x-2\right)$$
9). If a+b=5, ab=4 find the value of $$\Large a^{3}+b^{3}$$
 A). 60 B). 50 C). 56 D). 65
10). Simplify $$\Large \frac{x^{2}+11x+30}{ \left(x^{2}+2x-15\right) }$$
 A). $$\Large \frac{x+6}{x-3}$$ B). $$\Large \frac{x+3}{x-3}$$ C). $$\Large \frac{x+6}{x-5}$$ D). $$\Large \frac{x+5}{x+6}$$
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