Math

To simplify the algebraic expression, follow the order of operations by using the distributive property first and then combining like terms.

Step-by-Step Solution

Simplify (example 3)

  1. Distribute the coefficients outside each parenthesis

    • For the first term, distribute −2-2 to both terms inside (v+5)(v + 5):
      −2×v=−2v-2 \times v = -2v
      −2×5=−10-2 \times 5 = -10
      This expands to −2v−10-2v - 10.

    • For the second term, distribute 22 to both terms inside (2v−6)(2v - 6):
      2×2v=4v2 \times 2v = 4v
      2×(−6)=−122 \times (-6) = -12
      This expands to 4v−124v - 12.

  2. Combine the expanded terms

    • Write out the full expression after distribution:
      −2v−10+4v−12-2v - 10 + 4v - 12

  3. Combine like terms

    • Group and combine the variable terms containing vv:
      −2v+4v=2v-2v + 4v = 2v

    • Group and combine the constant numbers:
      −10−12=−22-10 - 12 = -22

  4. Write the final simplified expression

    • Combining these parts yields:
      2v−222v - 22


Example 4.


To simplify algebraic expressions, follow the order of operations by using the distributive property first and then combining like terms.

Step-by-Step Solution
Example 3

Simplify: −2(v+5)+2(2v−6)-2(v + 5) + 2(2v - 6)

  1. Distribute the coefficients outside each parenthesis

    • For the first term, distribute −2-2 to both terms inside (v+5)(v + 5):
      −2×v=−2v-2 \times v = -2v
      −2×5=−10-2 \times 5 = -10
      This expands to −2v−10-2v - 10.

    • For the second term, distribute 22 to both terms inside (2v−6)(2v - 6):
      2×2v=4v2 \times 2v = 4v
      2×(−6)=−122 \times (-6) = -12
      This expands to 4v−124v - 12.

  2. Combine the expanded terms

    • Write out the full expression after distribution:
      −2v−10+4v−12-2v - 10 + 4v - 12

  3. Combine like terms

    • Group and combine the variable terms containing vv:
      −2v+4v=2v-2v + 4v = 2v

    • Group and combine the constant numbers:
      −10−12=−22-10 - 12 = -22

  4. Write the final simplified expression

    • Combining these parts yields:
      2v−222v - 22

Example 4

Simplify: 5(2w+6)−12w5(2w + 6) - 12w

  1. Distribute the coefficient outside the parenthesis

    • Distribute 55 to both terms inside (2w+6)(2w + 6):
      5×2w=10w5 \times 2w = 10w
      5×6=305 \times 6 = 30
      This expands to 10w+3010w + 30.

  2. Combine the expanded terms

    • Write out the full expression after distribution:
      10w+30−12w10w + 30 - 12w

  3. Combine like terms

    • Group and combine the variable terms containing ww:
      10w−12w=−2w10w - 12w = -2w

    • Constant term remains:
      3030

  4. Write the final simplified expression

    • Combining these parts yields:
      −2w+30-2w + 30


Ej 6.


Simplify: −(u+6)+5u-(u + 6) + 5u

  1. Distribute the negative sign outside the parenthesis

    • Distribute −1-1 to both terms inside (u+6)(u + 6):
      −1×u=−u-1 \times u = -u
      −1×6=−6-1 \times 6 = -6
      This expands to −u−6-u - 6

  2. Combine the expanded terms

    • Write out the full expression after distribution:
      −u−6+5u-u - 6 + 5u

  3. Combine like terms

    • Group and combine the variable terms containing uu:
      −u+5u=4u-u + 5u = 4u

    • Constant term remains:
      −6-6

  4. Write the final simplified expression

    • Combining these parts yields:
      4u−64u - 6


Here are the step-by-step solutions for each example:

Example 3: −2(v+5)+2(2v−6)-2(v + 5) + 2(2v - 6)

  1. Distribute the coefficients outside each parenthesis:

    • −2×v=−2v-2 \times v = -2v

    • −2×5=−10-2 \times 5 = -10

    • 2×2v=4v2 \times 2v = 4v

    • 2×(−6)=−122 \times (-6) = -12

  2. Combine the expanded terms:

    • −2v−10+4v−12-2v - 10 + 4v - 12

  3. Combine like terms:

    • −2v+4v=2v-2v + 4v = 2v

    • −10−12=−22-10 - 12 = -22

  4. Final simplified expression:

    • 2v−222v - 22

Example 4: 5(2w+6)−12w5(2w + 6) - 12w

  1. Distribute the coefficient outside the parenthesis:

    • 5×2w=10w5 \times 2w = 10w

    • 5×6=305 \times 6 = 30

  2. Combine the expanded terms:

    • 10w+30−12w10w + 30 - 12w

  3. Combine like terms:

    • 10w−12w=−2w10w - 12w = -2w

  4. Final simplified expression:

    • −2w+30-2w + 30

Example 6: −(u+6)+5u-(u + 6) + 5u

  1. Distribute the negative sign outside the parenthesis:

    • −1×u=−u-1 \times u = -u

    • −1×6=−6-1 \times 6 = -6

  2. Combine the expanded terms:

    • −u−6+5u-u - 6 + 5u

  3. Combine like terms:

    • −u+5u=4u-u + 5u = 4u

  4. Final simplified expression:

    • 4u−64u - 6