University:
High School
Course:
High School Mathematics
Academic year:

2023
Views:

24

Pages:

2
Author:

anon

Adding and Subtracng Polynomials When adding or subtracting polynomials • Remove brackets (use integer rules to simplify the signs as well as the distributive prop erty) • Collect like terms Example 1: Simplify each expression a) (3x+4)+(8x+1) =3x+4+8x+1 =3x+8x+4+1 =11x+5 b) (2q-3)+(5q-2) =2q-3+5q-2 =2q+5q-3-2 =7q-5 c) (6r – 1) + (3r + 2) + (6r – 1) = 6r - 1 + 3r + 2 - 6r – 1 = 6r + 3r - 6r - 1 + 2 – 1 = 3r + 0 = 3r d) (5h+9) – (5h + 6) = 1(5h) + 1(9) - (- 5h) - (6) = 5h + 9 + 5h – 6 = 5h + 5h + 9 – 6 = 10h + 3 ( e) 2𝑥 2 2 ) ( 2 ) + 7𝑥 – 5 – 5𝑥 – 𝑥 + 6 2 =1(2𝑥 ) +1(7x) +1(-5)-1(5𝑥 )-1(-x)-1(6) use the distributie property =2x²+7x-5 -5x²+x-6 multiply double signs =2x²-5x²+7x+x-5-6 collect like terms =-3x² +8x-11 Example 2: The length of a rectangle is double the width plus 1 m. a) Draw a diagram of the rectangle. Label its sides. Let w represent the width of the rectangle and let Crepresent the width of the rectangle. l=2w+1 b) Find a simplified expression for the perimeter of the rectangle. P= l+w+l+w =2l+2w = 2(l + w) ∴P=2u+1+w+2w+1+w =2w+w+2w+w+1+1 =6w+2 OR P=2l+2w =2(2w+1)+2w =2(2w)+2(1)+2w =4w+2+2w =4w+2w+2 =6w+2 c) If the width is 4 m, what is the perimeter of the rectangle? -Substitute w=4 in P=6w+2 P=6(4)+2 =24+2 =26 ∴ The perimeter of the rectangle is 26m