IGCSE Math B 3.A Basic algebra processes Topic Practice

Given that $-3x^2+6x+2$ can be written in the form $a(x+b)^2+c$, where a, b and c are integers, find the value of a, the value of b and the value of c.

Simplify fully $\left(125 a^{9}\right)^{\frac{2}{3}}$

Simplify fully $\frac{(4xy^5)^3}{2xy}$.

Given that, for all values of x,
$$x^2+6x-15=(x+a)^2-b$$
where a and b are integers, find the value of a and the value of b.

Expand and simplify (4 x-5)(2 x+3)

Simplify fully $\frac{64 a^{3} b^{-1}}{4 a^{-2} b}$

Given that a is a positive integer, expand and simplify fully
$$\sqrt{5a}\left(\sqrt{20a}+a\sqrt{5a}\right).$$

Simplify $\frac{7}{4 x}+\frac{8}{3 x}-\frac{2}{5 x}$
Give your answer in its simplest form.

Simplify fully $\frac{36 x y^{2}}{12 x^{5} y^{7}}$