Math exercises on literal calculus and remarkable identities in ninth grade are always helpful. Thus, it will be necessary to develop and factor algebraic expressions. At the end of the exercises on literal calculation, you should be able to master this chapter.
Exercise 1: Literal calculation
- Reduce the following expressions:
| A = 3x – 8 + 4x + 5 | B = 3x² + 5x – 6 – 2x² -4x – 3 | C = 5x² – 7 – 9x² +x – 3x + 9 |
| D = 4x² – (5x + x² – 6x) + 7x | E = 3x – (4 + 2x) + (x² + 7) | F = 3x² – (4x – 1) – (x² +5x) |
- Substitute x for its value to calculate each literal expression:
| A = 7x – 3
For x = 5 |
B = x² + x – 9
For x = -2 |
C = -4x² – 2x + 2
For x = -3 |
| D = 2x – 7 + 3x + 1
For x = 4 |
E = (x – 3)²
For x = -4 |
F = (2x – 3)(6 – x²)
For x = 2 |
Exercise 2:
- Using the identity “k(a + b) = ka + kb”, develop the following expressions:
| A = 7(x + 4) | B = 4(3 – 2x) | C = -3(x + 7) |
| D = -5(3x – 2) | E = -2x(5 + 4x) | F = 3x²(1 – 2x) |
- Using the identity “(a + b)(c + d) = ac + ad + bc + bd”, develop the following expressions:
| A = (x + 2)(x + 3) | B = (x – 7)(3x – 2) | C = (1 + 2x)(3 – x) |
| D = (-7x + 6)(5 – x²) | E = (3x + 4)(-x + 1) | F = (3x² – 4)(2x + 5) |
- Write the square as a product and then expand the following expressions:
| A = (x + 2)² | B = (1 + x)² | C = (2x + 1)² |
| D = (3 + 2x)² | E = (3x + 2)² | F = (x² + 5)² |
- Write the square as a product and then expand the following expressions:
| A = (x – 2)² | B = (x – 7)² | C = (2x + 5)² |
| D = (-4x + 3)² | E = (3x – 2)² | F = (x² – 3)² |
- Using the identity “(a + b)(c + d) = ac + ad + bc + bd”, develop the following expressions:
| A = (x + 2)(x – 3) | B = (x – 7)(x + 7) | C = (2x – 5)(2x + 5) |
| D = (3 – 4x)(3 + 4x) | E = (x² – 3x)(x² + 3x) | F = (2x² + 4)(2x² – 4) |
Exercise 3:
Using the identity “ka + kb = k(a + b)”, factor the following expressions:
| A = 3x + 3y | B = 5x + 15 | C = 3 + 3a | |
| D = (2x + 1)(x + 4) + (2x + 1)(3x +2) | E = (x +7)² – (3x – 5)(x + 7) | ||
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