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Algebra - Simplifying algebraic expressions

Grade 7IGCSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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Definition of a Term: A term is a number, a variable, or a product of numbers and variables (e.g., 5, x, 3xy).

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Like Terms: Terms that have the exact same variables raised to the exact same powers. Only like terms can be added or subtracted.

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Coefficients: The numerical part of a term (e.g., in 7x27x^2, 7 is the coefficient).

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Expanding Brackets: Using the Distributive Law to multiply a term outside a bracket by every term inside.

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Order of Operations (BIDMAS/BODMAS): Always follow the order: Brackets, Indices, Division/Multiplication, and Addition/Subtraction.

📐Formulae

Distributive Law: a(b+c)=ab+aca(b + c) = ab + ac

Combining Like Terms: ax+bx=(a+b)xax + bx = (a + b)x

Multiplication Law: xm×xn=xm+nx^m \times x^n = x^{m+n}

Division Law: xm÷xn=xm−nx^m \div x^n = x^{m-n}

💡Examples

Problem 1:

Simplify 5x+3y−2x+7y5x + 3y - 2x + 7y

Solution:

3x+10y3x + 10y

Explanation:

Group the like terms together: (5x−2x)+(3y+7y)(5x - 2x) + (3y + 7y). Subtract the coefficients of x (5−2=35-2=3) and add the coefficients of y (3+7=103+7=10).

Problem 2:

Simplify 4a×3a24a \times 3a^2

Solution:

12a312a^3

Explanation:

Multiply the numerical coefficients (4×3=124 \times 3 = 12) and multiply the variables using index laws (a1×a2=a1+2=a3a^1 \times a^2 = a^{1+2} = a^3).

Problem 3:

Expand and simplify: 3(2x−4)+5x3(2x - 4) + 5x

Solution:

11x−1211x - 12

Explanation:

First, expand the bracket: 3×2x=6x3 \times 2x = 6x and 3×−4=−123 \times -4 = -12, resulting in 6x−12+5x6x - 12 + 5x. Then, combine the like terms: 6x+5x=11x6x + 5x = 11x.

Problem 4:

Simplify 10x52x2\frac{10x^5}{2x^2}

Solution:

5x35x^3

Explanation:

Divide the coefficients (10÷2=510 \div 2 = 5) and subtract the powers of the variables (5−2=35 - 2 = 3).