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].
