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# Basic Algebra

Simplify these algebraic expressions containing powers.

Use the Maths Symbols Pad for squared terms and square roots, etc.,

² ³ % x y z ( ) { } + - * / = ÷

This Maths pad will append characters to the active input. That is the question you are currently answering.

## 1 - Multiply out the brackets.

1. (2 + 3x)(3x – 1 )
____________   X
2. (3x + 2)(2x – 4)
____________   X
3. (x – 3 ) (4x + 1 )
____________   X
4. 4(x + 2y)(3x – 2y)
____________   X
5. 2(2x + y)(x – 2y)
____________   X
6. (3x + 2y)2
____________   X
² ³ % x y z ( ) { } + - * / = ÷

## 2 - The product of two terms.

Find the product of 5x — 2 and 3x + 2.

____________   X

## 3 - Square a term

Find the square of 2x — 1.

² ³ % x y z ( ) { } + - * / = ÷
____________   X

## 4 - Perimeters

Find a simplified expression for the perimeter and the area of the following shapes.

____________   X

____________   X

## 5 - Factorise and simplify.

Factorise and simplify the following:

1. 4xy²z + 8xyz²
____________   X
2. 8x²yz² + 12xy²z
____________   X
3. 8xyz + 16x²yz
____________   X
4. 20x²y²z² + 16xyz²
____________   X
² ³ % x y z ( ) { } + - * / = ÷

## 6 - Remove the negative powers - use positives

Rewrite the following without using negative powers:

1. k-²
____________   X
2. p-³q²
____________   X
3. gt-²
____________   X
4. l / (y-²)
____________   X
5. a-4 / v-²
____________   X
6. ( v-² x a4 ) / b
² ³ % x y z ( ) { } + - * / = ÷

## 7 - Simplify using positive numbers.

1. h² x h-8
____________   X
2. g / g4
____________   X
3. (t²)4 x (t³)-4 ) -4
____________   X
4. v-4 / v-²
____________   X
5. w4 / w5
6. ( a4 x a²) / (a5
____________   X
² ³ % x y z ( ) { } + - * / = ÷

## 8 - Simplify Powers

These expressions all involve fractional powers. Simplify them as far as possible.

1.   ____________   X
2.   ____________   X
3.   ____________   X
4.   ____________   X
5.   ____________   X
6.   ____________   X
7.   ____________   X
8.   ____________   X
9.   ____________   X
² ³ % x y z ( ) { } + - * / = ÷