Algebraic Expressions and Identities
Class 8 · Mathematics
4 ideas in Class 8 Mathematics, explained in plain words, with games and quizzes to practise.
Adding and Subtracting Algebraic Expressions
An algebraic expression is made of terms such as 3x or 5xy. Terms with the same letters and the same powers are like terms, and only like terms can be combined. For example, 4 apples and 3 apples make 7 apples, but 4 apples and 3 oranges stay separate. When we subtract, every sign in the second expression flips first.
Why it matters. Adding and subtracting expressions is the base for every later algebra skill. Children who mix up unlike terms or forget to flip signs when subtracting keep losing marks in equations and factorisation.
Try it in two minutes
- Take two coins and a few paper clips. Write 3c + 2k on one card and c + 5k on another, where c is a coin and k is a clip.
- Ask your child to add the cards by collecting coins together and clips together.
- Now subtract the second card from the first and ask what happens to the number of clips.
- Ask: why can we not add a coin and a clip into one pile?
Try at home. Write two short expressions with x and y and ask your child to add them and then subtract one from the other.
Multiplying Monomials
A monomial is an expression with only one term, such as 5x or 3ab². To multiply monomials, multiply the number parts together and then collect the letters, adding the powers of the same letter. So 5x times 4x² is 20x³, because x has power 1 in one monomial and 2 in the other.
Why it matters. This skill is used for areas and volumes written with letters. Children who multiply the powers instead of adding them, or forget the number part, will get wrong answers in many later chapters.
Try it in two minutes
- Draw a rectangle on paper and label the length 3x and the breadth 2y. Ask what the area is.
- Ask your child to multiply the numbers 3 and 2 first, then write the letters x and y beside the answer.
- Now make the breadth 2x. Ask what x times x looks like and why it is written x².
- Try three monomials, for example 2a, 3b and 4c, and ask whether the order matters.
Try at home. Give your child the box lengths 2a, 3a and 5a and ask for the volume as one monomial.
Multiplying a Monomial by a Polynomial
To multiply 3x by (5y + 2), we multiply 3x by each term inside the bracket and add: 15xy + 6x. This is the distributive law, the same idea as 7 × 106 being 7 × 100 plus 7 × 6. The monomial must multiply every term, not only the first.
Why it matters. Opening brackets correctly is needed in almost every algebra problem. A common mistake is multiplying only the first term, and another is a sign slip with negative terms.
Try it in two minutes
- Ask your child to find 6 × 104 by writing it as 6 × 100 plus 6 × 4.
- Now write 6 × (x + 4) and ask them to open the bracket in the same way.
- Try 2a × (3a - 5) and ask what 2a times -5 should be.
- Put a = 2 in the original and the answer and check that both give the same number.
Try at home. Ask your child to expand 4x(x + 3) and check the answer by putting x as 1 in both forms.
Multiplying Polynomials
To multiply (3a + 4b) by (2a + 3b), every term of the first bracket multiplies every term of the second. That gives 4 products, and two of them are like terms, so they combine into one term. A binomial times a trinomial gives 6 products before combining.
Why it matters. Multiplying brackets is a key step to solving equations and to factorising. Children who miss a product or forget to combine like terms lose track quickly.
Try it in two minutes
- Draw a grid with 2 rows and 2 columns on paper. Write x and 3 along the top and x and 2 down the side.
- Ask your child to fill each box with the product of its row and column labels.
- Add the four boxes together and ask which ones are like terms.
- Compare the result with (x + 3)(x + 2) multiplied out term by term.
Try at home. Ask your child to find (x + 4)(x + 5) with a grid and check by putting x as 1 into both forms.
What your child will practise
- Adding and Subtracting Algebraic Expressions: Lab Explorer Quest (Match It Up)
- Adding and Subtracting Algebraic Expressions: Ocean Quest (Flip and Match)
- Multiplying a Monomial by a Polynomial: Desert Quick Fire (Quick Fire)
- Multiplying Monomials: Mission Control Quest (Collect the Answer)
- Multiplying Polynomials: Desert Puzzle (Clue Puzzle)
- Quiz: Adding and Subtracting Algebraic Expressions (8 questions)
- Quiz: Multiplying Monomials (8 questions)
- Quiz: Multiplying Polynomials (8 questions)
- Quiz: Multiplying a Monomial by a Polynomial (8 questions)