IDNLearn.com offers a comprehensive solution for all your question and answer needs. Get the information you need from our community of experts who provide accurate and comprehensive answers to all your questions.

Evaluate the expression when [tex]a=4[/tex] and [tex]b=7[/tex].

[tex]\[ 2a^2 - 4b - 4a(b - a) = \, [?] \][/tex]


Sagot :

To evaluate the expression [tex]\(2a^2 - 4b - 4a(b - a)\)[/tex] when [tex]\(a = 4\)[/tex] and [tex]\(b = 7\)[/tex], follow these steps:

1. Calculate the first part:
[tex]\[ 2a^2 \][/tex]
Substitute [tex]\(a = 4\)[/tex]:
[tex]\[ 2(4^2) = 2 \times 16 = 32 \][/tex]

2. Calculate the second part:
[tex]\[ -4b \][/tex]
Substitute [tex]\(b = 7\)[/tex]:
[tex]\[ -4 \times 7 = -28 \][/tex]

3. Calculate the third part:
[tex]\[ -4a(b - a) \][/tex]
Substitute [tex]\(a = 4\)[/tex] and [tex]\(b = 7\)[/tex]:
[tex]\[ -4 \times 4 \times (7 - 4) = -4 \times 4 \times 3 = -48 \][/tex]

4. Add these parts together to find the result:
[tex]\[ 32 + (-28) + (-48) \][/tex]

Combine the terms:
[tex]\[ 32 - 28 - 48 = 4 - 48 = -44 \][/tex]

Thus, the value of the expression [tex]\(2a^2 - 4b - 4a(b - a)\)[/tex] when [tex]\(a = 4\)[/tex] and [tex]\(b = 7\)[/tex] is [tex]\(-44\)[/tex].

Breaking down further:
- The calculation for [tex]\(2a^2\)[/tex] gives [tex]\(32\)[/tex].
- The calculation for [tex]\(-4b\)[/tex] gives [tex]\(-28\)[/tex].
- The calculation for [tex]\(-4a(b - a)\)[/tex] gives [tex]\(-48\)[/tex].
- Summing these parts results in [tex]\(-44\)[/tex].

Therefore, the final expression [tex]\(2a^2 - 4b - 4a(b - a)\)[/tex] evaluates to [tex]\(-44\)[/tex].