Question

How do you simplify $(2x + 1)(x - 7)?$

Answer 1

Hint: As we know that we have to multiply the two give polynomials here. To multiply means to increase in number especially greatly or in multiples. Multiplicand refers to the number multiplied and multiplier refers to the number that multiplies the first number. Here in this question we have to find the product of two polynomials, we just multiply each term of the first polynomial by each term of the second polynomial and then simplify or if there is any algebraic identity possible we can apply that.

Complete step-by-step solution:
Here we have $(2x + 1)(x - 7)$
Now we will multiply each term of the first polynomial by each term of the second polynomial and then simplify or if there is any algebraic identity possible we can apply that.
So we can write: $2x(x - 7) + 1(x - 7)$
By multiplying it gives, $2{x^2} - 14x + x - 7$.
We will now add the similar terms i.e. $2{x^2} - 13x - 7$.
Hence the required answer is $2{x^2} - 13x - 7$.

Thus the correct answer is $2{x^2} - 13x - 7$.

Note: We should be careful while multiplying the polynomials and we should always be careful with the positive and negative signs as wrong signs can lead to wrong answers. We know that it can also be expanded as the term i.e. $(2x + 1)(x - 7)$ and the first $2x$ is multiplied with the second polynomial and then $( + 1)$ is multiplied with the second polynomial again, and then simplified. It will give the same result. Also we should be careful with the positive and negative sign as in the above solution as addition of positive and negative sign, always the greater sign is taken in the result.