What is (3+9+2)^2-(3-9-2)^2 ?

The solution to (3+9+2)^2-(3-9-2)^2 is 132

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(3+9+2)^2-(3-9-2)^2

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

132

Solution steps

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

Follow the PEMDAS order of operations

Calculate within parentheses

(3 + 9 + 2) : 14

3 + 9 + 2

3 + 9 + 2 = 14

= 14

= 1 4^{2} - (3 - 9 - 2)^{2}

Calculate within parentheses

(3 - 9 - 2) : - 8

3 - 9 - 2

Add and subtract (left to right)

3 - 9 = - 6

= - 6 - 2

- 6 - 2 = - 8

= - 8

= 1 4^{2} - (- 8)^{2}

Calculate exponents

1 4^{2} : 196

1 4^{2}

1 4^{2} = 196

= 196

= 196 - (- 8)^{2}

Calculate exponents

(- 8)^{2} : 64

(- 8)^{2}

Apply exponent rule:

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

n

is even

(- 8)^{2} = 8^{2} = 64

= 64

= 196 - 64

Add and subtract (left to right)

196 - 64 : 132

196 - 64

196 - 64 = 132

= 132

= 132

\frac{42}{2} \cdot (34 + 56)

(- 46) + (- 24) + (- 18)

\frac{3}{2} - \frac{3}{2} (1)

5 \times 1 \div 3

- 6 - 5 + 3 - 2 + 9 - 1