Mathematics, 17.07.2019 23:20 jhanezd

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

Answers: 2

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Answers

Answer from: lukeramjitsingh

$42^{2} -28^{2} =980$

Step-by-step explanation:

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

$a^{2} -b^{2} = (a+b)(a-b)$

Therefore

$42^{2} -28^{2} = (42-28)(42+28)$

Solving

(14)(70)=980

Answer from: nano792001

None

Step-by-step explanation:

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

Demonstration

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

$a^2-b^2=a^2-a\cdot b + a\cdot b - b^2$

Which can be simplified like this:

a^2-b^2=a^2-b^2

We have obtained the same result

Real problem

According to the problem 42^2 - 28^2 the development would be:

$42^2 - 28^2=(42+28)\cdot (42-28)$

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

$42^2 - 28^2=(70)\cdot (14)=980$

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

Answer from: Quest

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.

Answer from: Quest

sweetheart, there isn't a cube below.

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