Simplify (6x^2-1)+(x^2+3)-2(x^2-5)-15x^2

$(6 x^{2} - 1) + (x^{2} + 3) - 2 (x^{2} - 5) - 15 x^{2}$

Step 1

Remove parentheses.

$6 x^{2} - 1 + x^{2} + 3 - 2 (x^{2} - 5) - 15 x^{2}$

Step 2

Simplify each term.

Apply the distributive property.

$6 x^{2} - 1 + x^{2} + 3 - 2 x^{2} - 2 \cdot - 5 - 15 x^{2}$

Multiply $- 2$ by $- 5$ .

$6 x^{2} - 1 + x^{2} + 3 - 2 x^{2} + 10 - 15 x^{2}$

Step 3

Simplify by adding terms.

Add $6 x^{2}$ and $x^{2}$ .

$7 x^{2} - 1 + 3 - 2 x^{2} + 10 - 15 x^{2}$

Subtract $2 x^{2}$ from $7 x^{2}$ .

$5 x^{2} - 1 + 3 + 10 - 15 x^{2}$

Subtract $15 x^{2}$ from $5 x^{2}$ .

$- 10 x^{2} - 1 + 3 + 10$

Simplify by adding numbers.

Add $- 1$ and $3$ .

$- 10 x^{2} + 2 + 10$

Add $2$ and $10$ .

$- 10 x^{2} + 12$