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Like Terms

Like Terms. The area of the rectangle is the sum of the areas of the algebra tiles. The area of each square green tile is x² square units. The area of each long green tile is x square units. How many pieces make up the rectangle?

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Like Terms

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  1. Like Terms The area of the rectangle is the sum of the areas of the algebra tiles. The area of each square green tile is x² square units. The area of each long green tile is x square units. • How many pieces make up the rectangle? • Use each piece to write an expression for the area of the rectangle in terms of x² and x. • Use the idea that x+x+x = 3x. Terms that have the same variable parts are called LIKE TERMS. The terms 3x, 4x and 6x are like terms. Terms that have different variable parts are called UNLIKE TERMS. The terms 5x, 2x², 3y are unlike terms.

  2. Like Terms Example Simplify: 4x + 2y – 2x – 3y (Combine like terms.) 4x + 2y – 2x – 3y = 4x – 2x + 2y – 3y = 2x - y • Copy and Complete • 3x + 5x • 6a² - 3a² • 2t + 3t + 4t • 7w – 2w + 3w • 9c – 8c - c 6. Y + 5y – y 7. 6a + 9 + 7a – 3 8. 3x + 7x + 4x² + 3x² 9. 9 + 6b – b + 4b 10. x + y – x – y

  3. The Distributive Property The area of the large rectangle is the sum of the areas of the algebra tiles. The area of each long green tile is x square units. The area of each red tile is 1 square unit. 2 x 3 • Write an expression for the total area of the green tiles. • What is the total area of the red tiles? • Use the results from questions 1 and 2 to write an expression for the area of the large rectangle. To EXPAND an expression with brackets means to remove the brackets by multiplying. This is done using the DISTRIBUTIVE PROPERTY.

  4. The Distributive Property Example 3(y+2) Solution – multiply each term inside the brackets by 3. 3(y+2) = 3(y+2) = 3 x y + 3 x 2 = 3y + 6 • Solve • 5(t-3) • 7(m+1) • 4(a-7) • 4(4+m) • 8(x-4) 6. 7(3+t) 7. 2(3x + 2y) 8. 3(4a + 5b) 9. –3(3m – 2n) 10. –5(3s – t) 11. 4(3c – 2d + 5) 12. 5(x – 3 + 4y) 13. –6(2 + 3x + y) 14. –2(1 – x – y)

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