High School

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2.1 Simplify the following expressions:

2.1.1 \(6a + 5 + 4a - 2\)

2.1.2 \(5ab + 3ab - 2ab + 4\)

2.1.3 \(9p^3 + 4p^2 - p + 2p^2 + 2p - 5p^3\)

2.1.4 \(20k + 14f + k - 17f + 4\)

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QUESTION 3 - Multiplication with algebra.

Answer :

To simplify algebraic expressions, you combine like terms. Like terms are terms that have the same variables raised to the same power. Let's simplify each expression step-by-step.

2.1.1 Simplify [tex]6a + 5 + 4a - 2[/tex]:

  • Combine the like terms with the variable [tex]a[/tex]: [tex]6a + 4a = 10a[/tex].
  • Combine the constant terms: [tex]5 - 2 = 3[/tex].
  • The simplified expression is: [tex]10a + 3[/tex].

2.1.2 Simplify [tex]5ab + 3ab - 2ab + 4[/tex]:

  • Combine the like terms with the variable [tex]ab[/tex]: [tex]5ab + 3ab - 2ab = 6ab[/tex].
  • The "+ 4" is a constant term and cannot be combined with the terms involving [tex]ab[/tex].
  • The simplified expression is: [tex]6ab + 4[/tex].

2.1.3 Simplify [tex]9p^3 + 4p^2 - p + 2p^2 + 2p - 5p^3[/tex]:

  • Combine the like terms with [tex]p^3[/tex]: [tex]9p^3 - 5p^3 = 4p^3[/tex].
  • Combine the like terms with [tex]p^2[/tex]: [tex]4p^2 + 2p^2 = 6p^2[/tex].
  • Combine the like terms with [tex]p[/tex]: [tex]-p + 2p = p[/tex].
  • The simplified expression is: [tex]4p^3 + 6p^2 + p[/tex].

2.1.4 Simplify [tex]20k + 14f + k - 17f + 4[/tex]:

  • Combine the like terms with [tex]k[/tex]: [tex]20k + k = 21k[/tex].
  • Combine the like terms with [tex]f[/tex]: [tex]14f - 17f = -3f[/tex].
  • The constant term is [tex]+4[/tex], which stays as it is.
  • The simplified expression is: [tex]21k - 3f + 4[/tex].

These steps help make the expressions easier to work with by combining terms that share the same variables.

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