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In a difference of squares problem terms must be perfect squares?

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∙ 14y ago

Updated: 9/16/2023

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Q: In a difference of squares problem terms must be perfect squares?

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In a difference of squares problem both terms must be what squares?

Perfect

In a difference of squares problem both terms must be squares?

perfect * * * * * Not strictly. they could both be multiples of sqaures. For example, factorise 3x3 - 48x. Neither term is a square but they do become squares when the common factor, 3x, is separated out. Also, when rationalising surds, one would use the difference of two squares but (at least) one of the terms is not a square.

What does difference of perfect squares mean in math?

Given two integers, x and y, their squares are x^2 and y^2. The difference between them is called the difference of perfect squares and is (x^2-y^2) This is important because we can always factor this as (x+y)(x-y). We don't really need x and y to be integers, but in elementary algebra classes they often are. In reality, they can by any numbers. The idea behind this is when you multiply (x+y)(x-y) the xy and -xy terms cancel each other out and you are left with the x^2 and -y^2 terms.

When a variable term is multiplied by itself the product?

the different of two perfect squares can be formed by taking any two perfect squared terms

A definition of difference of squares?

A difference of two squared terms, i.e.:a2 - b2This form can be factored into (a + b)(a - b).

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Related Questions

In a difference of squares problem both terms must be what squares?

Perfect

In a difference of squares problem both terms must be squares?

perfect * * * * * Not strictly. they could both be multiples of sqaures. For example, factorise 3x3 - 48x. Neither term is a square but they do become squares when the common factor, 3x, is separated out. Also, when rationalising surds, one would use the difference of two squares but (at least) one of the terms is not a square.

How do you identify a difference of two squares?

The word "difference" implies subtraction. The word "squares" implies a perfect square term or number. To recognize the "difference of squares" look for 2 perfect square terms, one being subtracted from the other. Ex. x2 - 16. "x" is being squared and 16 is a perfect square. They are being subtracted. Factors: (x+4)(x-4)

The product of the sum and difference of two terms is equal to the what of the squares of the terms?

The difference.

What does difference of perfect squares mean in math?

Given two integers, x and y, their squares are x^2 and y^2. The difference between them is called the difference of perfect squares and is (x^2-y^2) This is important because we can always factor this as (x+y)(x-y). We don't really need x and y to be integers, but in elementary algebra classes they often are. In reality, they can by any numbers. The idea behind this is when you multiply (x+y)(x-y) the xy and -xy terms cancel each other out and you are left with the x^2 and -y^2 terms.

When a variable term is multiplied by itself the product?

the different of two perfect squares can be formed by taking any two perfect squared terms

A definition of difference of squares?

A difference of two squared terms, i.e.:a2 - b2This form can be factored into (a + b)(a - b).

How do you simplify an expression that has several terms?

There are several things you can do to simplify expressions. Specifically for expressions with several terms, two things you can do is to combine similar terms (terms that have the same combination of variables), and then (usually after combining), see if you can apply one of the common methods of factoring, such as looking for common factors, looking for a perfect cube, factoring the difference of squares, the sum or difference of cubes, etc.

What are the attributes of a polynomial expression that is a difference of squares?

All terms have even powers, factorable to the form (a+b)(a-b)

What is the smallest positive integer q for which 1008q is a perfect square?

In terms of prime factors, 1008 = 24*32*7 Then since 24 and 32 are perfect squares, all that is required is to make 7q a perfect square and so q = 7.

How do you determine if a polynomial is the difference of two squares?

"Difference" implies subtraction. Example: The difference of 8 and 5 is 3 because 8 - 5 = 3. To determine if a polynomial is the difference you probably have to subtract one polynomial from another and check if your answer matches a given polynomial. To clarify the above, the polynomial should be able to be factorised into two distinct factors. For example x^2 - y^2 = (x + y)(x - y). This is the difference of two squares.

What does difference mean in math terms?

difference means an answer to a subraction problem.

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