6th Grade Math Textbook, Fundamentals

Lesson 14-4 for exercise sets. &KDSWHU 

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Use algebra tiles to find the difference.
Write your answer in standard form.

1.(x 5 x^2 ) (2x^2  2 x) 2.(3  2 x^2 ) (xx^2 1)

Subtract algebraically. Use the horizontal or vertical method.

3.(17x18) (22x7) 4.(4x^2  4 x) (5x^2  5 x)

5.Discuss and WriteA rectangle has a length of (7c^2  7 c20) units.

Its width is (5c25) units shorter than its length. What polynomial

can express the rectangle’s width? Explain your answer.

• To subtract, add the opposite.


• The opposite (or additive inverse) of a
  polynomial is the product of the
  polynomial and 1.


• Apply the Distributive Property of
  Multiplication over Subtraction.
  Then simplify.


• Apply the Commutative and Associative
  Properties to group like terms.


• Combine like terms.

Method 2 Compute Vertically

• Align like terms in columns.


• Add the opposite of each term.

(19x^2  25 x) (7x^2  6 x)

(19x^2  25 x) [(7x^2  6 x)]

(19x^2  25 x) (1)(7x^2  6 x)

(19x^2  25 x) [1 • 7x^2 (1 • 6x)]

(19x^2  25 x) [ 7 x^2  ( 6 x)]

(19x^2  25 x)  ( 7 x^2  6 x)

[19x^2 ( 7 x^2 )][25x 6 x]

12 x^2  31 x

To subtract polynomials algebraically, add the opposite of the

polynomial being subtracted.

What is the difference of 19x^2  25 xand 7x^2  6 x?

To find the difference, subtract: (19x^2  25 x) (7x^2  6 x)

Use either the horizontal or vertical method.

Method 1 Compute Horizontally

19 x^2  25 x

(7x^2  6 x)

19 x^2  25 x

( 7 x^2  6 x)

12 x^2  31 x

So the difference of 19x^2  25 xand 7x^2  6 xis 12x^2  31 x.

Remember:

aba(b)

a1 • a

a(bc) abac