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2 years ago

Factorise 4a^2+b^2-4ab-8a+4b+4

Mathematics

1 answer:

Dima020 [189]2 years ago

6 0

Answer:

The factorized form of the given expression is $4 [(a-1)^2 - b(a - 1 + \frac{b}{4})]$

Step-by-step explanation:

Given;

4a² + b² - 4ab - 8a + 4b + 4

This expression is factorized as follows;

(4a² - 8a + 4) + (b² - 4ab + 4b)

(4a² - 4a - 4a + 4) + b² - 4b(a - 1)

(4a - 4)(a - 1) + b² - 4b(a - 1)

(4a - 4)(a - 1) - 4b(a - 1) + b²

4(a - 1)(a - 1) - 4b(a - 1) + b²

4(a - 1)² - 4b(a - 1 + b/4)

$4(a- 1)^2 - 4b(a - 1 + \frac{b}{4} )\\\\4 [(a-1)^2 - b(a - 1 + \frac{b}{4})]$

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Given f(x)=-2x-1, solve for x when f(x)=-7

Svetlanka [38]

Answer:

The answer is -15.

Step-by-step explanation:

1. 2x - 1

2. 2(-7) - 1

3. (-14) - 1

4. -15

By plugging in our x value, we are able to use PEMDAS to multiply 2 and the value of x and then, we subtract 1 from the value we got from step 3 to get -15.

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2 years ago

−2(2x+3)≤26 - 2 2 x + 3 ≤ 26 ?

SashulF [63]

$\huge \boxed{\mathbb{QUESTION} \downarrow}$

$- 2 ( 2 x + 3 ) \leq 26.$

$\large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}$

$- 2 ( 2 x + 3 ) \leq 26$

Divide both sides by -2. We know that since 2 is negative, it'll be < (less than) 0. So, the direction of inequality will change.

$2x+3\geq \frac{26}{-2} \\$

Divide 26 by -2..we'll get the answer as -13.

$2x+3\geq -13$

Now, subtract 3 from both the sides.

$2x\geq -13-3$

Subtracting -13 by 3..we'll get the answer as -16.

$2x\geq -16$

Divide both sides by 2. We know that since 2 is positive, the direction of inequality will remain the same.

$x\geq \frac{-16}{2} \\$

Divide -16 by 2..we'll get the answer as -8.

$\huge \boxed{ \boxed{ \bf \: x\geq -8 }}$

The correct answer is ⇨ x greater than or equal to -8.

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2 years ago

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Answer:

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2 years ago

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Answer:

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Step-by-step explanation:

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2 years ago

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These two scalene triangles are similar with a scale of 4:5. What is true about these figures?

disa [49]

Alright, lets get started.

Lets check each possible answer one by one.

We will start from option B.

BC is from small triangle and its corresponding side is DF, so its ratio will be $\frac{4}{5}$ not $\frac{5}{4}$ as given in option. Hence option B is incorrect.

For option C,

Angle a° and angle f° are not similar angles, if they were similar, then only their ratio will be 1 otherwise not 1. Hence option C is incorrect.

For option D,

Angle c° and angle f° are similar angles so, their ratio will be $\frac{c}{f} = 1$ . Hence option D is incorrect.

Now option A,

ED and AB are corresponding sides. ED is from bigger triangle and AB is from smaller triangle. Their ratio will be $\frac{ED}{AB} = \frac{5}{4}$ . Hence option A is correct answer.

Hope it will help :)

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2 years ago

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Factorise 4a^2+b^2-4ab-8a+4b+4​

Factorise 4a^2+b^2-4ab-8a+4b+4