Topic Details (Notes format)

How to Simplify Algebraic Expressions

Subject: Mathematics

Book: Maths Mastery

Simplifying algebraic expressions typically involves combining like terms, factoring out common factors, and applying distributive properties. For example, if you have 3x + 5x – 2y + y, you can group x terms and y terms: (3x + 5x) + (–2y + y) = 8x – y. Also, for expressions like 4a + 12b, factor out 4: 4(a + 3b). Simplification clarifies expressions and readies them for solving equations or inequalities. This skill is crucial for tackling advanced math—like polynomials, calculus, or system modeling—and fosters clear, methodical problem-solving strategies in both academics and real-life calculations.

Practice Questions

What is the sum of the first 10 positive even numbers?

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If a:b = 7:9 and b:c = 5:6, what is a:c?

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If the cost price of an item is Rs. 400 and the selling price is Rs. 500, what is the profit percentage?

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If x^2 - 6x + 9 = 0, what is the value of x?

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A train 120 meters long is moving at a speed of 54 km/h. How long will it take to pass a pole?

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What is the probability of drawing a king from a standard deck of 52 playing cards?

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The sides of a triangle are 13 cm, 14 cm, and 15 cm. What is its area?

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If a right triangle has legs of 9 cm and 12 cm, what is the length of the hypotenuse?

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If a+b = 10 and ab = 21, what is the value of (a-b)^2?

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A square is inscribed in a circle with a radius of 5 cm. What is the area of the square?

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