Simplify (x^2 - y^2)^2 when x=2 and y=-1

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justaguide | College Teacher | (Level 2) Distinguished Educator

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We have to simplify (x^2 - y^2)^2 when x = 2 and y = -1

Substitute x = 2 and y = -1 in the expression (x^2 - y^2)^2, we get:

(2^2 - (-1)^2)^2

= (4 - 1)^2

= 3^2

= 9

The required result is 9

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

This problem is a good reason to practice the simple products:

x^2 - y^2 is a difference of two squares and it returns the product (x-y)(x+y)

We'll replace x and y by the given values and we'll get:

(x^2 - y^2)^2 = [(x-y)(x+y)]^2 = [(2+1)(2-1)]^2 = [(3)*(1)]^2 = 3^2 = 9

We could also expand the binomial using the formula:

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

(x^2 - y^2)^2 = x^4 - 2x^2*y^2 + y^4

We'll replace x and y by the given values and we'll get:

(x^2 - y^2)^2 = 2^4 - 2*4*1 + 1 = 16 - 8 + 1 = 8+1 = 9

Therefore, the value of the given expression is 9.

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givingiswinning | Student, Grade 10 | (Level 1) Valedictorian

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(2^2 - (-1)^2) ^ 2

(4 - (1)) ^2

(3)^2

9

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atyourservice | Student, Grade 11 | (Level 3) Valedictorian

Posted on

 (x^2 - y^2)^2 when x=2 and y=-1

plug in x and y as their respective number

(2^2 - (-1)^2) ^ 2

(4 - (1)) ^2

(3)^2

9

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