Solve 4+3ab+4a+8b^2-2a(3b+4) | Microsoft Math Solver

Type a math problem

Evaluate

4 + 8 b^{2} - 4 a - 3 a b

Solution Steps

4 + 3 a b + 4 a + 8 b^{2} - 2 a (3 b + 4)

Multiply

- 1

and

2

to get

- 2

4 + 3 a b + 4 a + 8 b^{2} - 2 a (3 b + 4)

Use the distributive property to multiply

- 2 a

3 b + 4

4 + 3 a b + 4 a + 8 b^{2} - 6 a b - 8 a

Combine

3 a b

and

- 6 a b

to get

- 3 a b

4 - 3 a b + 4 a + 8 b^{2} - 8 a

Combine

4 a

and

- 8 a

to get

- 4 a

4 - 3 a b - 4 a + 8 b^{2}

Expand

4 + 8 b^{2} - 4 a - 3 a b

Solution Steps

4 + 3 a b + 4 a + 8 b^{2} - 2 a (3 b + 4)

Multiply

- 1

and

2

to get

- 2

4 + 3 a b + 4 a + 8 b^{2} - 2 a (3 b + 4)

Use the distributive property to multiply

- 2 a

3 b + 4

4 + 3 a b + 4 a + 8 b^{2} - 6 a b - 8 a

Combine

3 a b

and

- 6 a b

to get

- 3 a b

4 - 3 a b + 4 a + 8 b^{2} - 8 a

Combine

4 a

and

- 8 a

to get

- 4 a

4 - 3 a b - 4 a + 8 b^{2}

Quiz

Algebra

10 problems similar to:

4 + 3 a b + 4 a + 8 b^{2} - 2 a (3 b + 4)

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3 a^{2} + 4 a b + b^{2} - 2 a c - c^{2}

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3 a^{2} + 4 a b + b^{2} - 2 a c - c^{2} = (3 a + b + c) (a + b - c)

Explanation: Given:

3 a^{2} + 4 a b + b^{2} - 2 a c - c^{2}

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Although your working is correct, you won't be able to proceed further. The trick is to let

y = a^{2} + 2 a

. Then your expression becomes

y^{2} - 2 y - 3

= (y - 3) (y + 1)

= (a^{2} + 2 a - 3) (a^{2} + 2 a + 1)

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b^{2} - 4 a c = 16 p^{2} - 16 + 16 q^{2} = 16 (p^{2} - 1 + q^{2}) < 0

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4+3ab+4a+8b^{2}-2a\left(3b+4\right)

Multiply -1 and 2 to get -2.

4+3ab+4a+8b^{2}-6ab-8a

Use the distributive property to multiply -2a by 3b+4.

4-3ab+4a+8b^{2}-8a

Combine 3ab and -6ab to get -3ab.

4-3ab-4a+8b^{2}

Combine 4a and -8a to get -4a.

4+3ab+4a+8b^{2}-2a\left(3b+4\right)

Multiply -1 and 2 to get -2.

4+3ab+4a+8b^{2}-6ab-8a

Use the distributive property to multiply -2a by 3b+4.

4-3ab+4a+8b^{2}-8a

Combine 3ab and -6ab to get -3ab.

4-3ab-4a+8b^{2}

Combine 4a and -8a to get -4a.

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