Simplifying surds from $a\sqrt{b^2c}$ to $ab\sqrt{c}$, where $a$, $b$ and $c$ are positive integers.

Simplifying surds from $\sqrt{a^2b}$ to $a\sqrt{b}$, where $a$ and $b$ are positive integers.

Rewriting fractional expressions involving $\sqrt[n]{x^m}$ using rules to combine and simplify indices. 

Finding the product of a linear function of the form $mx+c$ and a cubic function of the form $ax^3+bx^2+cx+d$.

Finding the product of two linear functions of the form $mx+c$ and a quadratic function of the form $ax^2+bx+c$.

Finding the product of three linear functions of the form $mx+c$.

Finding the product of two linear functions of the form $mx+c$.

Given two quadratic expressions $f(x)$ and $g(x)$, calculate $f(x)(g(x)-f(x))$. 

Calculate the product of two quadratic expressions of the form $ax^2+bx+c$.

Calculating a quartic polynomial by squaring a quadratic expression of the form $ax^2+bx+c$.

Multiplying a linear expression of the form $mx+c$ by a quadratic expression of the form $ax^2+bx+c$. 

Finding linear combinations of two quadtratic expressions of the form $ax^2+bx+c$.

Collect like terms to simplify an algebraic expression. Part of HELM Book 1.3

Collect like terms to simplify an algebraic expression. Part of HELM Book 1.3

Simplify x^3+ax^2+bx^2+cx+dx+e to x^3 + (a+b)x^2 + (c+d)x + e

There are 6 versions of this question.

Part of HELM Book 1.3

Simplify x^2+yx+xy+y^2 to x^2 + 2xy + y^2.

There are 6 versions of this question.

Part of HELM Book 1.3

Identify that ax^2+by^2+cy+dx cannot be simplified.

There are 6 versions of this question.

Part of HELM Book 1.3

Simplify ax^2+bx^2+cx+d to (a+b)x^2 + cx + d

There are 6 versions of this question.

Part of HELM Book 1.3

Simplify ax^2+bx+cx+d to ax^2 + (b+c)x + d

There are 6 versions of this question.

Part of HELM Book 1.3

Simplify ax+b+cx+dy+e to (a+c)x + dy + b+e

There are 6 versions of this question.

Part of HELM Book 1.3

Given either (a) ax+bx+cy+dy, or (b) ax^2+bx+c, (c) ax^2+bx^2+cx^2, where a,b,c,d are randomised constants, and x and y are randomised letters, simplify by collecting like terms (if possible).

Part of HELM Book 1.3

Compare ax-bx, and ax(bx) and simplify, where a and b are +ve or -ve integers, and x is a randomised variable. Part of HELM Book 1.3

Part of HELM Book 1.2

Write an expression (a^k1*a^k2)/a^k3 using a single positive index. Variable a is randomised and can be a number or a letter. k1,k2 and k3 are randomised positive numbers.

Part of HELM Book 1.2

Collect like terms to simplify an algebraic expression. Part of HELM Book 1.3

Simplify three expressions: (a^b)^c, a^b * a^c, a^b/a^c where a, b and c are randomised. a is a letter, and b and c are rational numbers.

Part of HELM Book 1.2

Simplify (a^k1*a^k2)/(a^k3*a^k4) where a is a randomised variable and k1,k2,k3 and k4 are randomised fractions (k2 and/or k4 may be 0). They may be written in index form or in surd form, or even a combination of the two.

Part of HELM Book 1.2

Write an expression (a^k1*a^k2)/a^k3 using a single positive index. Variable a is randomised and can be a number or a letter. k1,k2 and k3 are randomised and can be positive or negative numbers.

Part of HELM Book 1.2

Simplify n1.v^k1.(n2.v^k2), where n1, n2 are positive integers, v is a random letter variable, and k1 and k2 are nonzero integers.

The answer should be expressed as n.v^k

Part of HELM Book 1.2

Use the index laws to simplify 3 simple expressions;

n^a*n^b, n^a/n^b, (n^a)^b, where n is a randomised variable or number, and a and b are randomised nonzero integers.

Part of HELM Book 1.2