Solve 3x(2x+3y)-(x-3y)(3x+4y)

$$3 x ( 2 x + 3 y ) - ( x - 3 y ) ( 3 x + 4 y )$$

Evaluate

$$3x^{2}+14xy+12y^{2}$$

Solution Steps

Use the distributive property to multiply 3x by 2x+3y.

$$6x^{2}+9xy-\left(x-3y\right)\left(3x+4y\right)$$

Apply the distributive property by multiplying each term of x-3y by each term of 3x+4y.

$$6x^{2}+9xy-\left(3x^{2}+4xy-9yx-12y^{2}\right)$$

Combine 4xy and -9yx to get -5xy.

$$6x^{2}+9xy-\left(3x^{2}-5xy-12y^{2}\right)$$

To find the opposite of 3x^{2}-5xy-12y^{2}, find the opposite of each term.

$$6x^{2}+9xy-3x^{2}-\left(-5xy\right)-\left(-12y^{2}\right)$$

The opposite of -5xy is 5xy.

$$6x^{2}+9xy-3x^{2}+5xy-\left(-12y^{2}\right)$$

The opposite of -12y^{2} is 12y^{2}.

$$6x^{2}+9xy-3x^{2}+5xy+12y^{2}$$

Combine 6x^{2} and -3x^{2} to get 3x^{2}.

$$3x^{2}+9xy+5xy+12y^{2}$$

Combine 9xy and 5xy to get 14xy.

$$3x^{2}+14xy+12y^{2}$$

Expand

$$3x^{2}+14xy+12y^{2}$$

Solution Steps

Use the distributive property to multiply 3x by 2x+3y.

$$6x^{2}+9xy-\left(x-3y\right)\left(3x+4y\right)$$

Apply the distributive property by multiplying each term of x-3y by each term of 3x+4y.

$$6x^{2}+9xy-\left(3x^{2}+4xy-9yx-12y^{2}\right)$$

Combine 4xy and -9yx to get -5xy.

$$6x^{2}+9xy-\left(3x^{2}-5xy-12y^{2}\right)$$

To find the opposite of 3x^{2}-5xy-12y^{2}, find the opposite of each term.

$$6x^{2}+9xy-3x^{2}-\left(-5xy\right)-\left(-12y^{2}\right)$$

The opposite of -5xy is 5xy.

$$6x^{2}+9xy-3x^{2}+5xy-\left(-12y^{2}\right)$$

The opposite of -12y^{2} is 12y^{2}.

$$6x^{2}+9xy-3x^{2}+5xy+12y^{2}$$

Combine 6x^{2} and -3x^{2} to get 3x^{2}.

$$3x^{2}+9xy+5xy+12y^{2}$$

Combine 9xy and 5xy to get 14xy.

$$3x^{2}+14xy+12y^{2}$$