Question

Which products result in a difference of squares? Check all that apply. (5z 3)(–5z – 3) (w – 2. 5)(w 2. 5) (8g 1)(8g 1) (–4v – 9)(–4v 9) (6y 7)(7y – 6) (p – 5)(p – 5).

Answer 1

The product of the two algebraic expression is a way to multiply these variables, coefficient and constants with each other. For the option 2 and 4 the result of the function is difference of the squares. Thus the option 2 and 4 are correct options.

Product of the algebraic expression-

Algebraic expression is a combination of the variables and coefficients. The product of the two algebraic expression is a way to multiply these variables, coefficient and constants with each other.

Given information-

1) The equation given in the option 1 is,

$(5z+3)(-5z-3)=-(5z+3)(5z+3)$

$(5z+3)(-5z-3)=-(5z+3)^2$

The result is not the difference of the square. Thus the option 1 is not correct.

2) The equation given in the option 2 is,

$(w-2.5)(w+2.5)$

In the algebra,

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

Use this formula for the above equation we get,

$(w-2.5)(w+2.5)=w^2-(2.5)^2$

The result is the difference of the square. Thus the option 2 is correct.

3) The equation given in the option 3 is,

$(8g+1)(8g+1)=(8g+1)^2$

The result is not the difference of the square. Thus the option 3 is not correct.

4) The equation given in the option 4 is,

$(-4v-9)(-4v+9)=-(4v+9)[-(4v-9)]$

$(-4v-9)(-4v+9)=(4v+9)(4v-9)$

$(-4v-9)(-4v+9)=4v^2-9^2$

The result is  the difference of the square. Thus the option 4 is correct.

5) The equation given in the option 5 is,

$(6y+7)(7y-6)=42y^2+13y-42$

The result is not the difference of the square. Thus the option 5 is not correct.

6) The equation given in the option 6 is,

$(p-5)(p-5)=(p-5)^2$

$(5z+3)(-5z-3)=-(5z+3)^2$

The result is not the difference of the square. Thus the option 6 is not correct.

Hence for the option 2 and 4 the result of the function is difference of the squares. Thus the option 2 and 4 are correct options.

Learn more about the product of the algebraic expression here;

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