mazielynn84
contestada

Is the polynomial a difference of squares?

Select Difference of squares or Not a difference of squares for each polynomial.

y^4−144
5m^2n^2−25
16x2−49
p^2−q^4

Respuesta :

calculista

Difference of squares are terms of the form

(a^2 - b^2) = (a+b)(a-b)

Case a

y^4−144 = (y^2 - 12) (y^2 + 12)  = (a-b)(a+b)

Difference of squares

Case b

5m^2n^2−25 = 5 (m^2 n^2 - 5) ≠ (a+b)(a-b)

Not a difference of squares

Case c

16x2−49 = (4 x - 7) (4 x + 7)  = (a-b)(a+b)

Difference of squares

Case d

p^2−q^4 = (p - q^2) (p + q^2) = (a-b)(a+b)

Difference of squares

abidemiokin

The only expression that is not a difference of two squares is [tex]5m^2n^2-25[/tex]The remaining expressions are differences of two squares.

Difference of two squares

The standard expression for the equation of difference of two squares is given as;

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

According to the question, we are to categorize the options as differences of squares or not.

For the expression [tex]y^4-144[/tex], this can be simplified as

[tex](y^2)^2-12^2 = (y^2-12)(y^2+12)[/tex]

The expression  y^2 - 144 is a difference of two square

For the expression [tex]6x^2 - 49[/tex], this can be simplified as;

[tex]16x^2-49=(4x)^2-7^2=(4x-7)(4x+7)\\[/tex]

Ths expression  16x^2 - 49 is a difference of two square

For the expression [tex]p^2-q^4[/tex], this is simplified as;

[tex]p^2-q^4=p^2-(q^2)^2=(p-q^2)(p+q^2)[/tex]

Ths expression  p^2 - q^4 is a difference of two square

The only expression that is not a difference of twwo squares is [tex]5m^2n^2-25[/tex]

Learn more on the difference of two square here: https://brainly.com/question/9239489

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