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Problems of the Day

This text provides examples and exercises for simplifying algebraic expressions using the Distributive Property and expanding binomials. It also includes a geometry problem on finding the area of shapes.

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Problems of the Day

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  1. Problems of the Day Simplify each expression. 1. (9s3t2)(−3st) 2. 5xy2(x + y) 3. 7mn(m2 + 10mn – 2) 4. d(−3d + 5) + 15d 5. 4w(5w – 4) + 3(w2 – 2w + 6) 6. x(x + 3) – 2(x – 7)= x(x + 8) −27s4t3 5x2y2 + 5xy3 7m3n + 70m2n2 – 14mn −3d2 + 20d 23w2 – 22w + 18 x = 2

  2. Algebra 1 ~ Chapter 8.7 Multiplying Polynomials

  3. To multiply a binomial by a binomial, you can apply the Distributive Property more than once. This is what is called EXPAND or EXPANDING! (x+3)(x + 2) = x(x + 2)+ 3(x + 2) = x(x + 2) + 3(x + 2) = x(x) + x(2) + 3(x) + 3(2) = x2 + 2x + 3x + 6 = x2 + 5x + 6

  4. Example 1 – Simplify each expression (x + 5)(x + 1) = x(x) + x(1) + 5(x) + 5(1) = x2 + 1x + 5x + 5 = x2 + 6x + 5 This expression is completely simplified. There are no like terms to combine.

  5. Example 2 – Simplify each expression (y + 3)(y – 7) = y(y) + y(-7) + 3(y) + 3(-7) = y2 + (-7y) + 3y + (-21) = y2 – 4y – 21 This expression is completely simplified. There are no like terms to combine.

  6. Example 3 – Simplify each expression (a–2)(a + 6) = a(a) + a(6) + -2(a) + -2(6) = a2 + 6a + (-2a) + (-12) = a2 + 4a – 12 This expression is completely simplified. There are no like terms to combine.

  7. Example 4 – Simplify each expression (x–4)(x – 5) = x(x) + x(-5) + -4(x) + -4(-5) = x2 + (-5x) + (-4x) + 20 = x2 – 9x + 20 This expression is completely simplified. There are no like terms to combine.

  8. Example 5 – Simplify each expression (2x+ 3)(6x + 5) = 2x(6x) + 2x(5) + 3(6x) + 3(5) = 12x2 + 10x + 18x + 15 = 12x2 + 28x + 15 This expression is completely simplified. There are no like terms to combine.

  9. Example 6 – Simplify each expression (2x+ 8)(5x – 4) = 2x(5x) + 2x(-4) + 8(5x) + 8(-4) = 10x2 + (-8x) + 40x + (-32) = 10x2 + 32x – 32 This expression is completely simplified. There are no like terms to combine.

  10. Example 7 – Simplify each expression (3x2–2)(4x2 –5x+ 9) = 3x2(4x2) + 3x2(-5x) + 3x2(9) -2(4x2) + -2(-5x)+ -2(9) = 12x4 + (-15x3) + 27x2 +(-8x2) + 10x +(-18) = 12x4 – 15x3 + 19x2 +10x – 18 This expression is completely simplified. There are no like terms to combine.

  11. Ex. 8 – Find the area of each shape below. (3x + 1) a.) b.) (4x – 3) (x + 4) (2x + 8) A = ½(b · h) A = ½(4x – 3)(2x + 8) = ½(8x2 + 32x – 6x – 24) = ½(8x2 + 26x – 24) A = 4x2 + 13x – 12 A = b · h A = (3x + 1)(x + 4) = 3x2 + 12x + 1x + 4 A = 3x2 + 13x + 4

  12. Lesson Wrap Up ~ Simplify each expression 1. (x + 2)(x – 8) 2. (a – 3)(a – 9) 3. (2x – 7)(5x – 4) 4. (3x – 5)(3x + 1) 5. Find the area of a triangle whose base is (6x + 4) and height is (x – 7). x2 – 6x – 16 a2 – 12a + 27 10x2 – 43x + 28 9x2 – 12x – 5 A = 3x2 – 19x – 14

  13. Assignment • Study Guide 8-7 (In-Class) • Skills Practice 8-7 (Homework)

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