Mathematics

Question

Which expressions are equivalent to 4(4a+5)4(4a+5) ? Choose 3 answers: Choose 3 answers: (Choice A, Checked) A 16a + 516a+5 (Choice B, Checked) B 16a+2016a+20 (Choice C) C 12a+20+4a12a+20+4a (Choice D) D 2(8a+10)2(8a+10) (Choice E) E 16a+5+416a+5+4

2 Answer

  • Answer:

                B, C, D

    Step-by-step explanation:

    I understand that you question is:

    Which expressions are equivalent to 4(4a+5)?

    Choose 3 answers:

    A 16a + 5

    B 16a+20

    C 12a+20+4a

    D 2(8a+10)

    E 16a+5+4

    Then:

    B, because:  

                      4(4a+5) = 4•4a + 4•5 = 16a + 20

    {distributive law}

    C, because:

                     4(4a+5) = 16a + 20 = 12a + 4a + 20 = 12a + 20 + 4a

    {distributive and associative laws}

    D, because:

                    4(4a+5) = 2•2(4a+5) = 2[2(4a+5)] = 2(2•4a + 2•5) = 2(8a + 10)

    {associative and distributive laws}

  • The required equivalent expressions for the expression 4(4a+5) are;

    1. 16a+20
    2. 2(8a+10)
    3. 12a + 20 + 4a

    Correct question

    Which expressions are equivalent to 4(4a+5)?

    Choose 3 answers:

    A 16a + 5

    B 16a+20

    C 12a+20+4a

    D 2(8a+10)

    E 16a+5+4

    Given the expression 4(4a+5)

    Given the values A, B, and C, according to the distributive law:

    A(B+C) = AB + AC

    Applying this to the given expression

    4(4a+5)

    = 4(4a) + 4(5)

    = 16a + 20 (First expression)

    Factoring out 2 from the result

    16a + 20

    = 2(8a) + 2(10)

    = 2(8a + 10) (Second expression)

    Rewriting equation 1

    From 1; 16a + 20

    16a + 20

    = (12a+4a) + 20

    = 12a + 20 + 4a (Third expression)

    Hence the required equivalent expressions for the expression 4(4a+5) are;

    1. 16a+20
    2. 2(8a+10)
    3. 12a + 20 + 4a

    Learn more here: https://brainly.com/question/1903897

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