What is 4(7-12)^2-2(1-4)^2 ?

The solution to 4(7-12)^2-2(1-4)^2 is 82

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4(7-12)^2-2(1-4)^2

4 (7 - 12)^{2} - 2 (1 - 4)^{2}

82

Solution steps

4 (7 - 12)^{2} - 2 (1 - 4)^{2}

Follow the PEMDAS order of operations

Calculate within parentheses

(7 - 12) : - 5

7 - 12

7 - 12 = - 5

= - 5

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

Calculate within parentheses

(1 - 4) : - 3

1 - 4

1 - 4 = - 3

= - 3

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

Calculate exponents

(- 5)^{2} : 25

(- 5)^{2}

Apply exponent rule:

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

n

is even

(- 5)^{2} = 5^{2} = 25

= 25

= 4 \cdot 25 - 2 (- 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 \cdot 25 - 2 \cdot 9

Multiply and divide (left to right)

4 \cdot 25 : 100

4 \cdot 25

4 \cdot 25 = 100

= 100

= 100 - 2 \cdot 9

Multiply and divide (left to right)

2 \cdot 9 : 18

2 \cdot 9

2 \cdot 9 = 18

= 18

= 100 - 18

Add and subtract (left to right)

100 - 18 : 82

100 - 18

100 - 18 = 82

= 82

= 82

- 4 - (- 7) + (- 8) + (- 11)

1^{2} + 1 - 2

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

6 \cdot 1 0^{2}

(2 \times + 3) (2 \times + 3)