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Chapter 8: Q7. (page 469)

Find each product.(x+4)(x鈭�1)

Short Answer

Expert verified

The product of the given expression is x2+3x鈭�4.

Step by step solution

01

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

  1. The product of two factors with like signs is positive, and the product of two factors with unlike signs is negative.
  2. If x is a variable and m, n are positive integers, then(xm脳xn)=xm+n
02

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.

(a+b)(c+d)=(a+b)脳(c+d)=a脳(c+d)+b脳(c+d)=(a脳c+a脳d)+(b脳c+b脳d)=(ac+ad)+(bc+bd)=ac+ad+bc+bd

03

Step 3. Substitute the values.

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

a=x,b=4,c=x,d=鈭�1

(x+4)(x鈭�1)=(x+4)(x+(鈭�1))=x(x+(鈭�1))+4(x+(鈭�1))=x2+x(鈭�1)+4x+4(鈭�1)=x2鈭�x+4x鈭�4=x2+3x鈭�4

Therefore, the product of the given expression is x2+3x鈭�4.

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Most popular questions from this chapter

Factor each trinomial, if possible. If the trinomial cannot be factored, write prime.

12x2+22x鈭�14.

MULTIPLE CHOICE A rectangle has a length that is 2 inches longer than its width. The area of the rectangle is 48 square inches. What is the length of the rectangle?

F 48 in.

G 8 in.

H 6 in.

J 2 in.

Solve each equation. Check your solution.

6p2鈭�3p=0

Solve each equation. Check your solutions.

16d2+40d+25=9

Factor each trinomial, if possible. If the polynomial cannot be factored, write prime.

x4鈭�1
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