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Simplify the expression. (5x + 3) - (2x + 3)

Solution:

(5x + 3) - (2x + 3) Now we have to multiply “–“ with the expression 2x + 3. So we get,

= 5x + 2- 2x - 3 5now we have to group the terms. So we get,

= 5x – 2x + 3 – 3

= 3x

**Example 2:**

Multiply the following terms (4x) ( 2x + 4).

**Solution:**

(4x) ( 2x + 4)Now we have to multiply 4x with 2x +4 like below.

= (4x `xx` 2x) + (4x `xx` 4) Note: (`a^m` ) (`a^n` ) = `a^(m+n)`

= 8`x^2` + 16x

**Example 3:**

Multiply the following terms (4`x^6` ) ( 5`x^8` `y^21` ).

**Solution:**

(4`x^6` ) ( 5`x^8` `y^21` ).we have to multiply 4`x^6` with 5`x^8` `y^21` like below.

= 4`x^6` `xx` 5`x^8` `y^21.`

= 4 `xx` 5 (`x^6` ) (`x^8` ) (`y^21` ) Note: (a^m) (a^n) = a^(m+n)

= 20 `x^(6+8)` `y^21`

= 20 `x^14 ` `y^21`

**Example 4:**

Find the intercepts for the following equation 6x + 3y = 7

**Solution:**

6x + 3y = 7

**X – Intercept:**

For finding the x – intercept, we have to plug-in y=0.

6x + 3(0) = 7

6x = 7 now we have to divide both sides by 6.

`(6x)/6` = 7/6

X = 1.17

**Y- intercept:**** **

For finding y- intercept, we have to plug-in x=0.

6(0) + 3y = 7

3y = 7 now we have to divide both sides by 3.

`(3y)/3 ` = 7/3

Y= 2.33

**Example 5:**

Factor the following expression 8`x^2` + 12x+4**.**

**Solution:**

8x^2 + 12x+4

Now we have to multiply the coefficient of the term 8`x^2` with the constant term 4. So we get

8 × 4 =32

Now we have to find the factor to 32. The factors are 4,8. By these factors, we can split out the term 11x as 7x + 4x. Therefore, the given equation become like below.

(8`x^2` + 8x) + (4x+4) Now we have to take out the common terms like below.

8x(x + 1) + 4(x +1)

(x + 1) (8x +4)

1. Subtract the following expression. (3x + 4) – (2x +3)

2. Multiply the following terms (3x) ( 4x + 2).

3. Multiply the following terms (6`x^5` `y^4` ) ( 8 `x^5` `y^4` ).

4. Find the intercepts for the following equation 7x + 7y = 7

5. Factor the following expression 9`x^2` + 14x+5**.**

**Answer key:**

- x + 1
- 12`x^2` + 6x
- 48 `x^10` `y^8`
- x – intercept = 1; y – intercept = 1
- (x + 1) (9x + 5)

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