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

The solution to (-2)^2-3(-2)(5)-(-3)^2 is 25

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

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

25

Solution steps

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

Follow the PEMDAS order of operations

Calculate exponents

(- 2)^{2} : 4

(- 2)^{2}

Apply exponent rule:

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

n

is even

(- 2)^{2} = 2^{2} = 4

= 4

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

Calculate exponents

(- 3)^{2} : 9

(- 3)^{2}

Apply exponent rule:

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

n

is even

(- 3)^{2} = 3^{2} = 9

= 9

= 4 - 3 (- 2) (5) - 9

Multiply and divide (left to right)

3 (- 2) (5) : - 30

3 (- 2) (5)

Apply rule

a \cdot (- b) = - a \cdot b

3 (- 2) = - 3 \cdot 2 = - 6

= - 6 (5)

Apply rule

(- a) \cdot (b) = - a \cdot b

(- 6) (5) = - 6 \cdot 5 = - 30

= - 30

= 4 - (- 30) - 9

Add and subtract (left to right)

4 - (- 30) - 9 : 25

4 - (- 30) - 9

Apply rule

- (- a) = + a

- (- 30) = + 30

= 4 + 30 - 9

4 + 30 = 34

= 34 - 9

34 - 9 = 25

= 25

= 25

2^{3} \cdot 3^{5}

\frac{1}{2} \cdot 7 (11 + 15)

8 - 32 + 6 - 3 + 15

(2)^{3} + 1

8 (6 - 5) + 10