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Algebra - Simplifying expressions (collecting like terms)

Grade 6Cambridge (IGCSE)

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

🔑Concepts

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A 'term' is a number, a variable, or a combination of both multiplied together (e.g., 55, xx, 3y3y).

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Like terms are terms that contain the exact same variables raised to the exact same powers.

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Only like terms can be added or subtracted to simplify an expression.

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The 'coefficient' is the number in front of the variable (e.g., in 4x4x, 44 is the coefficient).

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When simplifying, always look at the sign (+ or -) directly in front of the term to determine if you are adding or subtracting.

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Unlike terms (e.g., 3x3x and 5y5y) must remain separate and cannot be combined.

📐Formulae

ax+bx=(a+b)xax + bx = (a + b)x

ax−bx=(a−b)xax - bx = (a - b)x

x+x=2xx + x = 2x (Note: xx is the same as 1x1x)

a+b=b+aa + b = b + a (Commutative Law)

💡Examples

Problem 1:

Simplify 5x+3x+2x5x + 3x + 2x

Solution:

10x10x

Explanation:

All three terms are 'like terms' because they all contain the variable xx. We add the coefficients: 5+3+2=105 + 3 + 2 = 10.

Problem 2:

Simplify 7a+4b−2a+3b7a + 4b - 2a + 3b

Solution:

5a+7b5a + 7b

Explanation:

Group the like terms together: (7a−2a)+(4b+3b)(7a - 2a) + (4b + 3b). Solve each group: 7−2=5a7 - 2 = 5a and 4+3=7b4 + 3 = 7b.

Problem 3:

Simplify 3x2+5x−x2+2x3x^2 + 5x - x^2 + 2x

Solution:

2x2+7x2x^2 + 7x

Explanation:

x2x^2 and xx are NOT like terms because they have different powers. Group x2x^2 terms: 3x2−1x2=2x23x^2 - 1x^2 = 2x^2. Group xx terms: 5x+2x=7x5x + 2x = 7x.

Problem 4:

Simplify 10−4y+2−3y10 - 4y + 2 - 3y

Solution:

12−7y12 - 7y

Explanation:

Constants (numbers without variables) are like terms: 10+2=1210 + 2 = 12. The yy terms are −4y-4y and −3y-3y. Combining them: −4−3=−7-4 - 3 = -7, so we get −7y-7y.