Chapter 8: Q7. (page 469)

Find each product. $(x + 4) (x - 1)$

Short Answer

Expert verified

The product of the given expression is $x^{2} + 3 x - 4$ .

Step by step solution

Step 1. State the concept for multiplication of algebraic expressions.

The product of two factors with like signs is positive, and the product of two factors with unlike signs is negative.
If x is a variable and m, n are positive integers, then $(x^{m} \times x^{n}) = x^{m + n}$

Step 2. State multiplication of Two Binomials.

Let $(a + b)$ and $(c + d)$ are two binomials. By using the distributive law of multiplication over addition twice, their product as given below.

$\begin{matrix} (a + b) (c + d) = (a + b) \times (c + d) \\ = a \times (c + d) + b \times (c + d) \\ = (a \times c + a \times d) + (b \times c + b \times d) \\ = (a c + a d) + (b c + b d) \\ = a c + a d + b c + b d \end{matrix}$

Step 3. Substitute the values.

Substitute the values of a, b, c and d.

$a = x, b = 4, c = x, d = - 1$

$\begin{matrix} (x + 4) (x - 1) = (x + 4) (x + (- 1)) \\ = x (x + (- 1)) + 4 (x + (- 1)) \\ = x^{2} + x (- 1) + 4 x + 4 (- 1) \\ = x^{2} - x + 4 x - 4 \\ = x^{2} + 3 x - 4 \end{matrix}$

Therefore, the product of the given expression is $x^{2} + 3 x - 4$ .

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Find each product. $(x + 4) (x - 1)$

Short Answer

Step by step solution

Step 1. State the concept for multiplication of algebraic expressions.

Step 2. State multiplication of Two Binomials.

Step 3. Substitute the values.

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Find each product.(x+4)(x−1)

Short Answer

Step by step solution

Step 1. State the concept for multiplication of algebraic expressions.

Step 2. State multiplication of Two Binomials.

Step 3. Substitute the values.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Pure Maths

Theoretical and Mathematical Physics

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Find each product. $(x + 4) (x - 1)$