To determine which expression is equivalent to [tex]\(42x - 56y\)[/tex], we will simplify each given option and check if it matches the original expression.
Option A: [tex]\(7(6x - 8y)\)[/tex]
[tex]\[
7(6x - 8y) = 7 \cdot 6x - 7 \cdot 8y = 42x - 56y
\][/tex]
This simplifies directly to [tex]\(42x - 56y\)[/tex], which matches the original expression.
Option B: [tex]\(40(2x - 16y)\)[/tex]
[tex]\[
40(2x - 16y) = 40 \cdot 2x - 40 \cdot 16y = 80x - 640y
\][/tex]
This does not match the original expression [tex]\(42x - 56y\)[/tex].
Option C: [tex]\(14(x + 2x + 7y - 3y)\)[/tex]
[tex]\[
14(x + 2x + 7y - 3y) = 14(3x + 4y) = 14 \cdot 3x + 14 \cdot 4y = 42x + 56y
\][/tex]
This simplifies to [tex]\(42x + 56y\)[/tex], which does not match the original expression [tex]\(42x - 56y\)[/tex].
Option D: [tex]\(42(x + 14y)\)[/tex]
[tex]\[
42(x + 14y) = 42 \cdot x + 42 \cdot 14y = 42x + 588y
\][/tex]
This does not match the original expression [tex]\(42x - 56y\)[/tex].
Therefore, the expression that is equivalent to [tex]\(42x - 56y\)[/tex] is:
[tex]\[
\boxed{A}
\][/tex]
