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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:
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