Which shows 42^2 − 28^2 being evaluated using the difference of perfect squares method?


422 − 382 = (1,764 − 1,444)(1,764 + 1,444) = 1,283,200

422 − 382 = 1,764 − 1,444 = 400

422 − 382 = (42 − 38)2 = (4)2 = 16

422 − 382 = (42 + 38)(42 − 38) = (70)(4) = 280

Respuesta :

Answer:

[tex]42^{2} -28^{2} =980[/tex]

Step-by-step explanation:

If you evaluate the equation using the factorization method by difference of perfect squares, it would be done as follows

[tex]a^{2} -b^{2}  = (a+b)(a-b)[/tex]

Therefore

[tex]42^{2} -28^{2}   =   (42-28)(42+28)[/tex]

Solving

[tex](14)(70)=980[/tex]

Answer:

None

Step-by-step explanation:

The general form of the difference of perfect squares method is: [tex]a^2-b^2=(a+b)(a-b)[/tex]

Demonstration

The right part of the previous equation could be split like this:

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

Which can be simplified like this:

[tex]a^2-b^2=a^2-b^2[/tex]

We have obtained the same result

Real problem

According to the problem [tex]42^2 - 28^2[/tex] the development would be:

[tex]42^2 - 28^2=(42+28)\cdot (42-28)[/tex]

The idea is to solve each pair of parenthesis and then to multiply.

[tex]42^2 - 28^2=(70)\cdot (14)=980[/tex]

Thus, the result is not in the options because the problem asks for [tex]42^2 - 28^2[/tex] and the options are related to [tex]42^2 - 38^2[/tex]

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