Question

# Consider the difference of squares 𝑎^{2} − 𝑏^{2} for integers 𝑎 and 𝑏. Make a table for the difference of squares using consecutive integers for 𝑎 and 𝑏. What pattern do you notice? Using the pattern find the pair of consecutive integers that generate the difference of squares of –45.

Hint:

### The methods used to find the product of binomials are called special products.

Difference of squares is a case of a special product which occurs when we multiply a binomial by another binomial with the same terms but the opposite sign

## The correct answer is: 22 and 23

### a and b are consecutive integers. Let’s make a table for some pairs of a and b

We can notice that the difference of square of consecutive integers a and b is of the form -(a + b).

If the difference of two consecutive numbers is -45. We can think that there is only one case when a and b in -(a + b) is connective i.e. when a = 22 and b = 23.

Final Answer:

Hence, the pattern for difference of squares using consecutive integers for 𝑎 and 𝑏 is -(a + b) and the pair of consecutive integers that generate the difference of squares of –45 is 22 and 23

We can notice that the difference of square of consecutive integers a and b is of the form -(a + b).

If the difference of two consecutive numbers is -45. We can think that there is only one case when a and b in -(a + b) is connective i.e. when a = 22 and b = 23.

Final Answer:

Hence, the pattern for difference of squares using consecutive integers for 𝑎 and 𝑏 is -(a + b) and the pair of consecutive integers that generate the difference of squares of –45 is 22 and 23

### Related Questions to study

### The length of each side of a cube is 14𝑥 + 8 𝑓𝑒𝑒𝑡. Write a polynomial in standard form to represent the volume of the cube.

This question can be easily solved by using the formula

(a + b)3 = a3 + 3a2b + 3ab2 + b3

### The length of each side of a cube is 14𝑥 + 8 𝑓𝑒𝑒𝑡. Write a polynomial in standard form to represent the volume of the cube.

This question can be easily solved by using the formula

(a + b)3 = a3 + 3a2b + 3ab2 + b3

### The length of each side of a cube is 14𝑥 + 8 𝑓𝑒𝑒𝑡. Write a polynomial in standard form to represent the surface area of the cube.

This question can be easily solved by using the formula

(a + b)2 = a2 + 2ab + b2

### The length of each side of a cube is 14𝑥 + 8 𝑓𝑒𝑒𝑡. Write a polynomial in standard form to represent the surface area of the cube.

This question can be easily solved by using the formula

(a + b)2 = a2 + 2ab + b2