Extra Practice 3
Lesson 5.3: Adding Polynomials
1.
Use algebra tiles to model each sum. Sketch your tile model.
Record your answer symbolically.
a) (– 4h + 1) + (6h + 3)
b) (2a2 + a) + (–5a2 + 3a)
c) (3y2 – 2y + 5) + (–y2 + 6y + 3)
d) (3 – 2y + y2) + (–1 + y – 3y2)
2.
Add these polynomials. Use algebra tiles if it helps.
a) (x – 5) + (2x + 2)
b) (b2 + 3b) + (b2 – 3b)
2
2
c) (y + 6y) + (–7y + 2y)
d) (5n2 + 5) + (–1 – 3n2)
3.
Add these polynomials. Use algebra tiles if it helps.
a) (–7x + 5)
b) (4x2 – 3)
+ (2x – 8)
+ (–8x2 – 1)
c)
(x2 – 4x + 3)
+ (–x2 – 2x – 3)
d) (3x2 – 4x + 1)
+ (–2x2 + 4x + 1)
4.
Add.
a) (y2 + 6y – 5) + (–7y2 + 2y – 2)
c) (3m2 + m) + (–10m2 – m – 2)
5.
a) For each shape below, write the perimeter as a sum of polynomials and in simplest form.
i)
ii)
iii)
b) (–2n + 2n2 + 2) + (–1 – 7n2 + n)
d) (–3d2 + 2) + (–2 – 7d2 + d)
iv)
b) Use substitution to check each answer in part a.
6.
The sum of two polynomials is 4r + 5 – 3r2. One polynomial is –8 – 2r2 + 2r; what is the
other polynomial? Explain how you found your answer.
Master 5.22
Extra Practice 4
Lesson 5.4: Subtracting Polynomials
1.
Use algebra tiles. Sketch your tile model. Record your answer symbolically.
a) (4x + 2) – (2x + 1)
b) (4x + 2) – (–2x +1)
c) (4x + 2) – (2x – 1)
d) (4x + 2) – (–2x – 1)
2.
Use algebra tiles to model find each difference. Sketch your tile model. Record your answer
symbolically.
a) (2s2 + 3s + 6) – (s2 + s + 2)
b) (2s2 + 3s – 6) – (s2 + s – 2)
2
2
c) (–2s + 3s + 6) – (–s + s + 2)
d) (2s2 – 3s + 6) – (s2 – s + 2)
3.
Use a personal strategy to subtract. Check your answers by adding.
a) (2x + 3) – (5x + 4)
b) (4 – 8w) – (7w + 1)
2
2
c) (x + 2x – 4) – (4x + 2x – 2)
d) (–9z2 – z – 2) – (3z2 – z – 3)
4.
A student subtracted
(3y2 + 5y + 2) – (4y2 + 3y + 2) like this:
= 3y2 – 5y – 2 – 4y2 – 3y – 2
= 3y2 – 4y2 – 5y – 3y – 2 – 2
= –y2 – 8y – 4
a) Explain why the student’s solution is incorrect.
b) What is the correct answer? Show your work.
5.
The difference between two polynomials is (5x + 3). One of the two polynomials is
(4x + 1 – 3x2). What is the other polynomial? Explain how you found your answer.
6.
Subtract.
a) (mn – 5m – 7) – (–6n + 2m + 1)
b) (2a + 3b – 3a2 + b2) – (–a2 + 8b2 + 3a – b)
c) (xy – x – 5y + 4y2) – (6y2 + 9y – xy)
Extra Practice 3 – Master 5.21
Lesson 5.3
1. a) 2h + 4
2
b) –3a + 4a
2
c) 2y + 4y + 8
d) 2 – y – 2y
2
2
2. a) 3x – 3
2
c) –6y + 8y
b) 2b
2
d) 2n + 4
3. a) –5x – 3
c) –6x
b) –4x – 4
2
d) x + 2
2
2
4. a) –6y + 8y – 7
2
c) –7m – 2
2
b) –n – 5n + 1
2
d) –10d + d
5. a) i) (2n + 2) + (n + 1) + (2n + 2) + (n + 1)
= 6n + 6
ii) (3p + 4) + (3p + 4) + (3p + 4) = 9p + 12
iii) (4y + 1) + (4y + 1) + (4y + 1) + (4y + 1)
= 16y + 4
iv) (a + 8) + (a + 3) + (12) = 2a + 23
b) i) 2(1) + 2 + 1 + 1 + 2(1) + 2 + 1 + 1 = 12
6(1) + 6 = 12
ii) 3(1) + 4 + 3(1) + 4 + 3(1) + 4 = 21
9(1) + 12 = 21
iii) 4(1) + 1 + 4(1) + 1+ 4(1) + 1+ 4(1) + 1
= 20
16(1) + 4 = 20
iv) 1 + 8 + 1 + 3 + 12 = 25
2(1) + 23 = 25
2
2
2
6. (4r + 5 – 3r ) – (–8 – 2r + 2r) = 13 – r + 2r
Extra Practice 4 – Master 5.22
Lesson 5.4
1. a) 2x + 1;
2
b) 6x + 1;
d) s – 2s + 4;
c) 2x + 3;
3. a) –3x – 1
2
c) –3x – 2
d) 6x + 3;
2
2. a) s + 2s + 4
b) 3 – 15w
2
d) –12z + 1
4. a) The student is incorrect because he
changed the signs in the first polynomial.
2
2
b) (3y + 5y + 2) – (4y + 3y + 2)
2
2
= 3y + 5y + 2 – 4y – 3y – 2
2
2
= 3y – 4y + 5y – 3y + 2 – 2
2
= –y + 2y
5. There are two possible answers.
2
2
(4x + 1 – 3x ) – (5x + 3) = –3x – x – 2, or
2
2
(5x + 3) + (4x + 1 – 3x ) = –3x + 9x + 4
2
b) s + 2s – 4;
2
c) –s + 2s + 4;
6. a) mn – 7m – 8 + 6n
2
2
b) –a + 4b – 2a – 7b
2
c) 2xy – x – 14y – 2y