Answer:
Tank which is capable of holding 1 can fill each one of the tanks an exact number of time.
Step-by-step explanation:
Three tanks are capable of holding
To find which tank can be used to fill each one of them an exact number of time, find
Therefore,
So, tank which is capable of holding 1 can fill each one of the tanks an exact number of time.
Answer:
1. (4a+3)(4a-3)
2. (2m + 5)(2m-5)
3. (4b-5)²
4. (2x-1)²
5. (3x+1)(3x-1)
6. (n+5)(n-5)
7. (n²-10)²
8. (a²+3)(a²-3)
9. (k²+6)(k²-6)
10. (n²+7)(n²-7)
Step-by-step explanation:
For special products like these, just remember the
Difference of Squares formula:
and
Square of difference formula:
1. 16a²-9 follows the difference of squares form:
a² - b² = (a+b)(a-b)
So all we need to do is get the square root of a and b and follow the form:
(√16a²) - (√9) = (4a +3) (4a - 3)
Let's check through FOIL:
(4a +3) (4a - 3)
16a² - 12a + 12a - 9
16a² - 9
2. 4m² - 25 also follows the same form of difference of squares:
(√4m²) - (√25) = (2m +5) (2m - 5)
Let's check!
(2m +5) (2m - 5)
4m² + 10m - 10m -25
4m² - 25
3. 16b² - 40b + 25 follows the form of square of difference:
a² - 2ab + b² = (a - b)²
√16b² = 4b
√25 = 5
(4b - 5)²
Let's check!
(4b-5)(4b - 5)
16b² - 20b - 20b + 25
16b² - 40b + 25
HEre's another way to look at it:
First multiply the coefficients of the first and last term:
16 x 25 = 400
Next think of two numbers that when you multiply them, you will come up with 400 and sum up to -40. The two numbers would be -20 and -20 which will be the middle term
So it would fill in this way:
16b² - 20b - 20b + 25
Factor the equation:
(16b² - 20b) (-20b + 25)
4b(4b-5) - 5(4b-5)
(4b-5)(4b-5) = (4b-5)²
4. 4x² - 4x + 1 follows that same form:
√4x² = 2x
√1 = 1
(2x - 1)²
Let's check!
(2x - 1)(2x - 1)
4x² - 2x - 2x + 1
4x²- 4x + 1
5. 9x² - 1 follows the form of difference of squares:
√9x² - √1 = (3x + 1)(3x - 1)
Let's check!
(3x + 1)(3x - 1)
9x² + 3x - 3x - 1
9x² - 1
6. n² - 25 follows the form of difference of squares:
√n² - √25 = (n + 5)(n - 5)
Let's check!
(n + 5)(n - 5)
n² + 5n - 5n - 25
n² - 25
7. n⁴ - 100
√n⁴ - √100 = (n² + 10)(n² - 100)
Let's check!
(n² + 10)(n² - 100)
n⁴ + 10n² - 10n² -100
n⁴ - 100
8. a⁴ - 9
√a⁴ - √9 = (a² + 3)(a² - 3)
Let's check!
(a² + 3)(a² - 3)
a⁴ + 3a² - 3a² - 9
a⁴ - 9
9. k⁴ - 36
√k⁴ - √36 = (k² + 6) (k² - 6)
Let's check!
(k² + 6) (k² - 6)
k⁴ + 6k² - 6k² - 36
k⁴ - 36
10. n⁴ - 49
√n⁴ - √49 = (n² + 7) (n² - 7)
Let's check!
(n² + 7) (n² - 7)
n⁴ +7n² - 7n²- 49
n⁴ - 49