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3 years ago

16(a+b)^2-49(a-b)^2 factorize the expression

Mathematics

1 answer:

noname [10]3 years ago

4 0

The given expression is a difference of squares, so we have

16 (a + b)² - 49 (a - b)² = 4² (a + b)² - 7² (a - b)²

… = (4 (a + b))² - (7 (a - b))²

… = (4 (a + b) - 7 (a - b)) (4 (a + b) + 7 (a - b))

… = (4a + 4b - 7a + 7b) (4a + 4b + 7a - 7b)

… = (-3a + 11b) (11a - 3b)

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3 years ago

Is my solution correct?

nlexa [21]

Hello there!

Yes, your solution is correct! A way to check it is replacing the value you found for x into x in the equation.

3(2-x) = 7 - 4x ⇒ 3(2-1) = 7 - 4(1)

And now solve 3(2-1) = 7 - 4(1).

3(1) = 7 - 4(1)

3 = 7 - 4

3 = 3

Since it is a true statement that 3 is equal to 3, it means your solution of x = 1 is correct. Good job! :)

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A paddleboat can move at a speed of 4 km/h in still water. The boat is paddled 12 km downstream in a river in the same time it

Bas_tet [7]

Answer:

Speed of the river = $\frac{4}{3}$ km per hour

Step-by-step explanation:

Speed of the boat in still water = 4 km per hour

Let the speed of the river = v km per hour

Speed of the boat upstream = (4 - v) km per hour

Time taken to cover 6 km = $\frac{\text{Distance}}{\text{Speed}}$

= $\frac{6}{4-v}$ hours

Speed of the boat downstream = (4 + v) km per hour

Time taken to cover 12 km = $\frac{12}{4+v}$ hours

Since, time taken by the boat in both the cases is same,

$\frac{6}{4-v}= \frac{12}{4+v}$

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12v + 6v = 48 - 24

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v = $\frac{24}{18}$

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3 years ago

16(a+b)^2-49(a-b)^2 factorize the expression​

16(a+b)^2-49(a-b)^2 factorize the expression