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)
= a2 - ab + ab - b2
= a2 - b2
Final Answer:
The product of (𝑎 + 𝑏) and (𝑎 − 𝑏) is a2 - b2 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.
The constant term in the product (𝑥 + 3) (𝑥 + 4) is
The constant term in the product (𝑥 + 3) (𝑥 + 4) is
Write the product in standard form. (3𝑦 − 5)(3𝑦 + 5)
This question can be easily solved by using the formula
(a + b)(a - b) = a2 - b2
Write the product in standard form. (3𝑦 − 5)(3𝑦 + 5)
This question can be easily solved by using the formula
(a + b)(a - b) = a2 - b2
Write the product in standard form. (𝑥 − 4)(𝑥 + 4)
This question can be easily solved by using the formula
(a + b)(a - b) = a2 - b2
Write the product in standard form. (𝑥 − 4)(𝑥 + 4)
This question can be easily solved by using the formula
(a + b)(a - b) = a2 - b2
The area of the rectangle is 𝑥2 + 11𝑥 + 28. Its length is x + __ and its width is __+ 4. Find the missing terms in the length and the width.
The area of the rectangle is 𝑥2 + 11𝑥 + 28. Its length is x + __ and its width is __+ 4. Find the missing terms in the length and the width.
Simplify: 12 - [13a - 4(5a -7) - 8 {2a -(20a - 3a)}]
Simplify: 12 - [13a - 4(5a -7) - 8 {2a -(20a - 3a)}]
Write the product in standard form. (2𝑥 + 5)2
This question can be easily solved by using the formula
(a + b)2 = a2 + 2ab + b2
Write the product in standard form. (2𝑥 + 5)2
This question can be easily solved by using the formula
(a + b)2 = a2 + 2ab + b2
Write the product in standard form. (𝑥 − 7)2
This question can be easily solved by using the formula
(a - b)2 = a2 - 2ab + b2
Write the product in standard form. (𝑥 − 7)2
This question can be easily solved by using the formula
(a - b)2 = a2 - 2ab + b2
(𝑥 + 9)(𝑥 + 9) =
This question can be easily solved by using the formula
(a + b)2 = a2 + 2ab + b2
(𝑥 + 9)(𝑥 + 9) =
This question can be easily solved by using the formula
(a + b)2 = a2 + 2ab + b2
Find the area of the rectangle.
Find the area of the rectangle.
The table below shows the distance a train traveled over time. How can you determine the equation that represents this relationships.
The table below shows the distance a train traveled over time. How can you determine the equation that represents this relationships.
Simplify: 4x2(7x -5) -6x2(2 -4x)+ 18x3
Simplify: 4x2(7x -5) -6x2(2 -4x)+ 18x3
(𝑎 + (−3))2 =
This question can be easily solved by using the formula
(a - b)2 = a2 - 2ab + b2
(𝑎 + (−3))2 =
This question can be easily solved by using the formula
(a - b)2 = a2 - 2ab + b2
Use the table method to multiply a binomial with a trinomial.
(−3𝑥2 + 1) (2𝑥2 + 3𝑥 − 4)
Use the table method to multiply a binomial with a trinomial.
(−3𝑥2 + 1) (2𝑥2 + 3𝑥 − 4)
(𝑥 − 2)2 =
This question can be easily solved by using the formula
(a - b)2 = a2 - 2ab + b2
(𝑥 − 2)2 =
This question can be easily solved by using the formula
(a - b)2 = a2 - 2ab + b2