Question

# Why the product of two binomials (𝑎 + 𝑏) and (𝑎 − 𝑏) is a binomial instead of a trinomial?

Hint:

### A polynomial equation with two terms usually joined by a plus or minus sign is called a binomial.

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: a2 - b2

### Let’s first the product of (𝑎 + 𝑏) and (𝑎 − 𝑏)

(a + b)(a - b) = a(a - b) + b(a - b)

= a(a) + a(-b) + b(a) + b(-b)

= a^{2} - ab + ab - b^{2}

= a^{2} - b^{2}

Final Answer:

The product of (𝑎 + 𝑏) and (𝑎 − 𝑏) is a^{2} - b^{2} which has only two terms and hence it is a binomial.

### Related Questions to study

### Graph the equation

We can find the tabular values for any points of x and then plot them on the graph. But we usually choose values for which calculating y is easier. This makes plotting the graph simpler. We can also find the values by putting different values of y in the equation to get different values for x. Either way, we need points satisfying the equation to plot its graph.

### Graph the equation

We can find the tabular values for any points of x and then plot them on the graph. But we usually choose values for which calculating y is easier. This makes plotting the graph simpler. We can also find the values by putting different values of y in the equation to get different values for x. Either way, we need points satisfying the equation to plot its graph.

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(a + b)(a - b) = a2 - b2

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This question can be easily solved by using the formula

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

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This question can be easily solved by using the formula

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

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This question can be easily solved by using the formula

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

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

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This question can be easily solved by using the formula

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