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Basic Algebra

Simplify these algebraic expressions containing powers.

Multiply out the brackets and simplify your answers where possible:
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 ) ____________
  2. (3x + 2)(2x – 4) ____________
  3. (x – 3 ) (4x + 1 ) ____________
  4. 4(x + 2y)(3x – 2y) ____________
  5. 2(2x + y)(x – 2y) ____________
  6. (3x + 2y)2 ____________
² ³ % x y z ( ) { } + - * / = ÷

2 - The product of two terms.

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

____________

3 - Square a term

Find the square of 2x — 1.

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

4 - Perimeters

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


IMAGE ____________
IMAGE ____________

5 - Factorise and simplify.

Factorise and simplify the following:

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

6 - Remove the negative powers - use positives

Rewrite the following without using negative powers:

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

7 - Simplify using positive numbers.

Simplify the following and write your answer without using negative powers:

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

8 - Simplify Powers

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

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

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