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Simplify: [tex]\((7x + 2)(7x - 2)\)[/tex]

A. [tex]\(49x^2 - 4\)[/tex]
B. [tex]\(49x^2 + 28x - 4\)[/tex]
C. [tex]\(49x^2 + 4\)[/tex]
D. [tex]\(49x^2 - 28x - 4\)[/tex]

Sagot :

GinnyAnswer
To simplify the expression [tex]\((7x + 2)(7x - 2)\)[/tex], we can apply the difference of squares formula, which states that:

[tex]\[ (a + b)(a - b) = a^2 - b^2 \][/tex]

Here, we have [tex]\(a = 7x\)[/tex] and [tex]\(b = 2\)[/tex]. Substituting these values into the formula:

[tex]\[ (7x + 2)(7x - 2) = (7x)^2 - (2)^2 \][/tex]

Now compute the squares separately:

[tex]\[ (7x)^2 = 49x^2 \][/tex]
[tex]\[ (2)^2 = 4 \][/tex]

Substituting these back into the expression, we get:

[tex]\[ (7x + 2)(7x - 2) = 49x^2 - 4 \][/tex]

Therefore, the simplified expression is:

[tex]\[ 49x^2 - 4 \][/tex]

Among the given options, the correct one is:

[tex]\[ \boxed{49 x^2 - 4} \][/tex]
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