What is 5(4-5)^2+3(5-1)-2(1+2)^2(2)+2(3)(4) ?

The solution to 5(4-5)^2+3(5-1)-2(1+2)^2(2)+2(3)(4) is 5

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5(4-5)^2+3(5-1)-2(1+2)^2(2)+2(3)(4)

5 (4 - 5)^{2} + 3 (5 - 1) - 2 (1 + 2)^{2} (2) + 2 (3) (4)

5

Solution steps

5 (4 - 5)^{2} + 3 (5 - 1) - 2 (1 + 2)^{2} (2) + 2 (3) (4)

Follow the PEMDAS order of operations

Calculate within parentheses

(4 - 5) : - 1

4 - 5

4 - 5 = - 1

= - 1

= 5 (- 1)^{2} + 3 (5 - 1) - 2 (1 + 2)^{2} (2) + 2 (3) (4)

Calculate within parentheses

(5 - 1) : 4

5 - 1

5 - 1 = 4

= 4

= 5 (- 1)^{2} + 3 \cdot 4 - 2 (1 + 2)^{2} (2) + 2 (3) (4)

Calculate within parentheses

(1 + 2) : 3

1 + 2

1 + 2 = 3

= 3

= 5 (- 1)^{2} + 3 \cdot 4 - 2 \cdot 3^{2} (2) + 2 (3) (4)

Calculate exponents

(- 1)^{2} : 1

(- 1)^{2}

Apply exponent rule:

(- a)^{n} = a^{n},

n

is even

(- 1)^{2} = 1^{2} = 1

= 1

= 5 \cdot 1 + 3 \cdot 4 - 2 \cdot 3^{2} (2) + 2 (3) (4)

Calculate exponents

3^{2} : 9

3^{2}

3^{2} = 9

= 9

= 5 \cdot 1 + 3 \cdot 4 - 2 \cdot 9 (2) + 2 (3) (4)

Multiply and divide (left to right)

5 \cdot 1 : 5

5 \cdot 1

5 \cdot 1 = 5

= 5

= 5 + 3 \cdot 4 - 2 \cdot 9 (2) + 2 (3) (4)

Multiply and divide (left to right)

3 \cdot 4 : 12

3 \cdot 4

3 \cdot 4 = 12

= 12

= 5 + 12 - 2 \cdot 9 (2) + 2 (3) (4)

Multiply and divide (left to right)

2 \cdot 9 (2) : 36

2 \cdot 9 (2)

2 \cdot 9 = 18

= 18 (2)

18 (2) = 36

18 (2)

Apply rule:

(a) = a

(2) = 2

= 18 \cdot 2

Multiply the numbers:

18 \cdot 2 = 36

= 36

= 36

= 5 + 12 - 36 + 2 (3) (4)

Multiply and divide (left to right)

2 (3) (4) : 24

2 (3) (4)

2 (3) = 6

2 (3)

Apply rule:

(a) = a

(3) = 3

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6

= 6 (4)

6 (4) = 24

6 (4)

Apply rule:

(a) = a

(4) = 4

= 6 \cdot 4

Multiply the numbers:

6 \cdot 4 = 24

= 24

= 24

= 5 + 12 - 36 + 24

Add and subtract (left to right)

5 + 12 - 36 + 24 : 5

5 + 12 - 36 + 24

5 + 12 = 17

= 17 - 36 + 24

17 - 36 = - 19

= - 19 + 24

- 19 + 24 = 5

= 5

= 5

(3) - (6) + (- 5) - (- 8)

- 4^{4} \cdot (- 2^{5})

2 (1)^{2} - 2

- 6 + 4 - 3

34 - 18 - (- 23)

What is 5(4-5)^2+3(5-1)-2(1+2)^2(2)+2(3)(4) ?
The solution to 5(4-5)^2+3(5-1)-2(1+2)^2(2)+2(3)(4) is 5