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

The solution to (2+3)^2-(3-5)^3 is 33

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

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

33

Solution steps

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

Follow the PEMDAS order of operations

Calculate within parentheses

(2 + 3) : 5

2 + 3

2 + 3 = 5

= 5

= 5^{2} - (3 - 5)^{3}

Calculate within parentheses

(3 - 5) : - 2

3 - 5

3 - 5 = - 2

= - 2

= 5^{2} - (- 2)^{3}

Calculate exponents

5^{2} : 25

5^{2}

5^{2} = 25

= 25

= 25 - (- 2)^{3}

Calculate exponents

(- 2)^{3} : - 8

(- 2)^{3}

Apply exponent rule:

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

n

is odd

(- 2)^{3} = - 2^{3} = - 8

= - 8

= 25 - (- 8)

Add and subtract (left to right)

25 - (- 8) : 33

25 - (- 8)

Apply rule

- (- a) = + a

- (- 8) = + 8

= 25 + 8

25 + 8 = 33

= 33

= 33

((- 10 + 6) - (- 4 - 2)) + (6 - (3 - 1))

(9 + 2 \times 5 + 1) \div 4 + 4 \times (6 - 8 \div 2)

4^{0} + 3

7^{2} \times 1 - 5 \div 3

4^{0} - 3