Factorise:
1.\({a}^{2}-9\)
2.\({m}^{2}-36\)
3.\(9{b}^{2}-81\)
4.\(16{b}^{6}-25{a}^{2}\)
5.\({m}^{2}-\frac{1}{9}\)
7.\(16b{a}^{4}-81b\)
8.\({a}^{2}-10a+25\)
10.\(2{a}^{2}-12ab+18{b}^{2}\)
11.$-4{b}{2}-144{b}{8}+48{b}^{5
12.\((16-{x}^{4})\)
13.\({7x}^{2}-14x+7xy-14y\)
14.\({y}^{2}-7y-30\)
15.\(1-x-{x}^{2}+{x}^{3}\)
16.\(-3(1-{p}^{2})+p+1\)
17.\(x-x^{3} + y - y^{3}\)
18.\(x^{2} - 2x + 1 - y^{4}\)
19.\(4b(x^{3} - 1) + x(1-x^{3})\)
20.\(3p^{3} - \frac{1}{9}\)
21.\(8x^6-125y^9\)
22.\((2+p)^3- 8(p+1)^3\)
Simplify the following:
1.\({(a-2)}^{2}-a(a+4)\)
2.\((5a-4b)(25{a}^{2}+20ab+16{b}^{2})\)
3.\((2m-3)(4{m}^{2}+9)(2m+3)\)
4.\((a+2b-c)(a+2b+c)\)
5.\(\dfrac{{p}^{2}-{q}^{2}}{p}รท\dfrac{p+q}{{p}^{2}-pq}\)
6.\(\dfrac{2}{x}+\dfrac{x}{2}-\dfrac{2x}{3}\)
7.\(\dfrac{1}{a+7}-\dfrac{a+7}{a^{2}-49}\)
8.\(\dfrac{x+2}{2x^{3}} + 16\)
9.\(\dfrac{1-2a}{4a^{2} -1} - \dfrac{a-1}{2a^{2}-3a+1} - \dfrac{1}{1-a}\)
10.\(\dfrac{x^{2} + 2x}{x^{2}+ x + 6} \times \dfrac{x^{2} + 2x + 1}{x^{2} + 3x +2}\)
Show that \({(2x-1)}^{2}-{(x-3)}^{2}\) can be simplified to \((x+2)(3x-4)\).
What must be added to \({x}^{2}-x+4\) to make it equal to \({(x+2)}^{2}\)?
Evaluate \(\dfrac{x^{3}+1}{x^{2}-x+1}\) if \(x=7,85\) without using a calculator. Show your work.
With what expression must \((a-2b)\) be multiplied to get a product of \(a^3-8b^3\)?
With what expression must \(27x^3+1\) be divided to get a quotient of \(3x+1\)?