Expand $(2x - 7)(2x - 5)$.
(A) To expand the expression $(2x - 7)(2x - 5)$,we use the distributive property ($FOIL$ method):
$1$. Multiply the first terms: $(2x) \times (2x) = 4x^2$.
$2$. Multiply the outer terms: $(2x) \times (-5) = -10x$.
$3$. Multiply the inner terms: $(-7) \times (2x) = -14x$.
$4$. Multiply the last terms: $(-7) \times (-5) = 35$.
Combining these results: $4x^2 - 10x - 14x + 35 = 4x^2 - 24x + 35$.
$1$. Multiply the first terms: $(2x) \times (2x) = 4x^2$.
$2$. Multiply the outer terms: $(2x) \times (-5) = -10x$.
$3$. Multiply the inner terms: $(-7) \times (2x) = -14x$.
$4$. Multiply the last terms: $(-7) \times (-5) = 35$.
Combining these results: $4x^2 - 10x - 14x + 35 = 4x^2 - 24x + 35$.
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