Solve 3*(7x^2-3x+4)-(2x^2-13x+6)+(3x^2+8)+5

$$3 \cdot ( 7 x ^ { 2 } - 3 x + 4 ) - ( 2 x ^ { 2 } - 13 x + 6 ) + ( 3 x ^ { 2 } + 8 ) + 5$$

Evaluate

$$22x^{2}+4x+19$$

Solution Steps

Use the distributive property to multiply 3 by 7x^{2}-3x+4.

$$21x^{2}-9x+12-\left(2x^{2}-13x+6\right)+3x^{2}+8+5$$

To find the opposite of 2x^{2}-13x+6, find the opposite of each term.

$$21x^{2}-9x+12-2x^{2}+13x-6+3x^{2}+8+5$$

Combine 21x^{2} and -2x^{2} to get 19x^{2}.

$$19x^{2}-9x+12+13x-6+3x^{2}+8+5$$

Combine -9x and 13x to get 4x.

$$19x^{2}+4x+12-6+3x^{2}+8+5$$

Subtract 6 from 12 to get 6.

$$19x^{2}+4x+6+3x^{2}+8+5$$

Combine 19x^{2} and 3x^{2} to get 22x^{2}.

$$22x^{2}+4x+6+8+5$$

Add 6 and 8 to get 14.

$$22x^{2}+4x+14+5$$

Add 14 and 5 to get 19.

$$22x^{2}+4x+19$$

Expand

$$22x^{2}+4x+19$$

Solution Steps

Use the distributive property to multiply 3 by 7x^{2}-3x+4.

$$21x^{2}-9x+12-\left(2x^{2}-13x+6\right)+3x^{2}+8+5$$

To find the opposite of 2x^{2}-13x+6, find the opposite of each term.

$$21x^{2}-9x+12-2x^{2}+13x-6+3x^{2}+8+5$$

Combine 21x^{2} and -2x^{2} to get 19x^{2}.

$$19x^{2}-9x+12+13x-6+3x^{2}+8+5$$

Combine -9x and 13x to get 4x.

$$19x^{2}+4x+12-6+3x^{2}+8+5$$

Subtract 6 from 12 to get 6.

$$19x^{2}+4x+6+3x^{2}+8+5$$

Combine 19x^{2} and 3x^{2} to get 22x^{2}.

$$22x^{2}+4x+6+8+5$$

Add 6 and 8 to get 14.

$$22x^{2}+4x+14+5$$

Add 14 and 5 to get 19.

$$22x^{2}+4x+19$$