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Factor Linear Expressions

Grade 7 · Algebra · Worksheet 1

  1. Factor the expression: 54x + 72y = ? Answer: ______________
  2. A community center is planning a mural project that requires rectangular panels. The total area needed for all panels can be expressed as 42x + 56 square feet, where x represents the length of each panel in feet. To determine the standard width that will work for all panels, the director needs to factor this expression using the greatest common factor. What is the factored form of 42x + 56? Answer: ______________
  3. Factor the expression: 18x + 24y = ? Answer: ______________
  4. A community center is planning to create rectangular activity zones for their summer program. The total area needed for all zones can be expressed as 42x + 56 square meters, where x represents the length of each zone in meters. The director needs to factor this expression to determine the standard width that will work for all zones. What is the factored form of the expression 42x + 56 using the greatest common factor? Answer: ______________
  5. Factor: 144x - 96 = ? Answer: ______________
  6. A community center is planning to create identical care packages for senior citizens. They have collected 144 boxes of tea and 96 packages of cookies to distribute equally among the packages. What is the greatest number of identical care packages they can create where each package contains the same number of tea boxes and cookie packages, with no items left over? Answer: ______________
  7. A community center is planning a mural project that requires rectangular panels. The total area needed for the mural can be expressed as 42x + 63 square feet, where x represents the length of each panel section in feet. The project manager needs to factor this expression to determine the standard width that will work for all panels. What is the greatest common factor of the terms in the expression 42x + 63? Answer: ______________
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Answer Key & Explanations

Factor Linear Expressions · Grade 7 · Worksheet 1

  1. Factor the expression: 54x + 72y = ? Answer: 18(3x + 4y) Solution: Find the greatest common factor (GCF) of 54 and 72. List the factors of 54: 1, 2, 3, 6, 9, 18, 27, 54 List the factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 The largest common factor is 18.
    Full step-by-step solution

    Step 1: Find the greatest common factor (GCF) of 54 and 72. Step 2: List the factors of 54: 1, 2, 3, 6, 9, 18, 27, 54 Step 3: List the factors of 72: 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72 Step 4: The largest common factor is 18. Step 5: Divide each term by 18: 54x ÷ 18 = 3x, 72y ÷ 18 = 4y Step 6: Write the factored expression: 18(3x + 4y) The answer is 18(3x + 4y).

  2. A community center is planning a mural project that requires rectangular panels. The total area needed for all panels can be expressed as 42x + 56 square feet, where x represents the length of each panel in feet. To determine the standard width that will work for all panels, the director needs to factor this expression using the greatest common factor. What is the factored form of 42x + 56? Answer: 14(3x + 4) Solution: Identify the terms in the expression: 42x and 56 Find the greatest common factor of 42 and 56 List the factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 List the factors of 56: 1, 2, 4, 7, 8, 14, 28, 56 The common factors are 1, 2, 7, 14.
    Full step-by-step solution

    Step 1: Identify the terms in the expression: 42x and 56 Step 2: Find the greatest common factor of 42 and 56 Step 3: List the factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 Step 4: List the factors of 56: 1, 2, 4, 7, 8, 14, 28, 56 Step 5: The common factors are 1, 2, 7, 14. The greatest is 14 Step 6: Factor out 14 from each term: 42x ÷ 14 = 3x and 56 ÷ 14 = 4 Step 7: Write the factored form: 14(3x + 4) The factored form is 14(3x + 4).

  3. Factor the expression: 18x + 24y = ? Answer: 6(3x + 4y) Solution: Identify the coefficients of the terms. The coefficients are 18 (from 18x) and 24 (from 24y). Find the greatest common factor (GCF) of 18 and 24.
    Full step-by-step solution

    Let's factor the expression 18x + 24y step by step. Step 1: Identify the coefficients of the terms. The coefficients are 18 (from 18x) and 24 (from 24y). Step 2: Find the greatest common factor (GCF) of 18 and 24. List the factors: Factors of 18: 1, 2, 3, 6, 9, 18 Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 The largest common factor is 6. Step 3: Factor out the GCF (6) from each term. 18x divided by 6 is 3x. 24y divided by 6 is 4y. Step 4: Write the expression as the GCF multiplied by the remaining sum. 18x + 24y = 6 * (3x) + 6 * (4y) = 6(3x + 4y) Final answer: 6(3x + 4y)

  4. A community center is planning to create rectangular activity zones for their summer program. The total area needed for all zones can be expressed as 42x + 56 square meters, where x represents the length of each zone in meters. The director needs to factor this expression to determine the standard width that will work for all zones. What is the factored form of the expression 42x + 56 using the greatest common factor? Answer: 14(3x + 4) Solution: Identify the terms in the expression: 42x and 56 Find the greatest common factor of 42 and 56 List the factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 List the factors of 56: 1, 2, 4, 7, 8, 14, 28, 56 The common factors are 1, 2, 7, and 14 The greatest common factor is 14 Divide each term by 14: 42x ÷…
    Full step-by-step solution

    Step 1: Identify the terms in the expression: 42x and 56 Step 2: Find the greatest common factor of 42 and 56 Step 3: List the factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 Step 4: List the factors of 56: 1, 2, 4, 7, 8, 14, 28, 56 Step 5: The common factors are 1, 2, 7, and 14 Step 6: The greatest common factor is 14 Step 7: Divide each term by 14: 42x ÷ 14 = 3x, 56 ÷ 14 = 4 Step 8: Write the factored form: 14(3x + 4) The factored form is 14(3x + 4).

  5. Factor: 144x - 96 = ? Answer: 48(3x - 2) Solution: Identify the terms: 144x and -96. Find the GCF of 144 and 96. Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 The greatest common factor is 48.
    Full step-by-step solution

    Step 1: Identify the terms: 144x and -96. Step 2: Find the GCF of 144 and 96. Factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 The greatest common factor is 48. Step 3: Divide each term by the GCF. 144x ÷ 48 = 3x -96 ÷ 48 = -2 Step 4: Write the factored form: 48(3x - 2). The answer is 48(3x - 2).

  6. A community center is planning to create identical care packages for senior citizens. They have collected 144 boxes of tea and 96 packages of cookies to distribute equally among the packages. What is the greatest number of identical care packages they can create where each package contains the same number of tea boxes and cookie packages, with no items left over? Answer: 48 Solution: Identify the two quantities: 144 boxes of tea and 96 packages of cookies Find the greatest common factor (GCF) of 144 and 96 List the factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 List the factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 Identify the common factors:…
    Full step-by-step solution

    Step 1: Identify the two quantities: 144 boxes of tea and 96 packages of cookies Step 2: Find the greatest common factor (GCF) of 144 and 96 Step 3: List the factors of 144: 1, 2, 3, 4, 6, 8, 9, 12, 16, 18, 24, 36, 48, 72, 144 Step 4: List the factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96 Step 5: Identify the common factors: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48 Step 6: The greatest common factor is 48 Step 7: Check: 144 ÷ 48 = 3 tea boxes per package, 96 ÷ 48 = 2 cookie packages per package The answer is 48.

  7. A community center is planning a mural project that requires rectangular panels. The total area needed for the mural can be expressed as 42x + 63 square feet, where x represents the length of each panel section in feet. The project manager needs to factor this expression to determine the standard width that will work for all panels. What is the greatest common factor of the terms in the expression 42x + 63? Answer: 21 Solution: Identify the coefficients in the expression 42x + 63. The coefficients are 42 and 63.
    Full step-by-step solution

    Step 1: Identify the coefficients in the expression 42x + 63. The coefficients are 42 and 63. Step 2: Find the factors of 42: 1, 2, 3, 6, 7, 14, 21, 42 Step 3: Find the factors of 63: 1, 3, 7, 9, 21, 63 Step 4: Identify the common factors: 1, 3, 7, 21 Step 5: The greatest common factor is 21. The answer is 21.