Solve (x+3y)(4x+8y)+(9x+27y)(16x+32y)

$$(x+3y)(4x+8y)+(9x+27y)(16x+32y)$$

Evaluate

$$148\left(x+2y\right)\left(x+3y\right)$$

Solution Steps

Apply the distributive property by multiplying each term of x+3y by each term of 4x+8y.

$$4x^{2}+8xy+12yx+24y^{2}+\left(9x+27y\right)\left(16x+32y\right)$$

Combine 8xy and 12yx to get 20xy.

$$4x^{2}+20xy+24y^{2}+\left(9x+27y\right)\left(16x+32y\right)$$

Apply the distributive property by multiplying each term of 9x+27y by each term of 16x+32y.

$$4x^{2}+20xy+24y^{2}+144x^{2}+288xy+432yx+864y^{2}$$

Combine 288xy and 432yx to get 720xy.

$$4x^{2}+20xy+24y^{2}+144x^{2}+720xy+864y^{2}$$

Combine 4x^{2} and 144x^{2} to get 148x^{2}.

$$148x^{2}+20xy+24y^{2}+720xy+864y^{2}$$

Combine 20xy and 720xy to get 740xy.

$$148x^{2}+740xy+24y^{2}+864y^{2}$$

Combine 24y^{2} and 864y^{2} to get 888y^{2}.

$$148x^{2}+740xy+888y^{2}$$

Expand

$$148x^{2}+740xy+888y^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of x+3y by each term of 4x+8y.

$$4x^{2}+8xy+12yx+24y^{2}+\left(9x+27y\right)\left(16x+32y\right)$$

Combine 8xy and 12yx to get 20xy.

$$4x^{2}+20xy+24y^{2}+\left(9x+27y\right)\left(16x+32y\right)$$

Apply the distributive property by multiplying each term of 9x+27y by each term of 16x+32y.

$$4x^{2}+20xy+24y^{2}+144x^{2}+288xy+432yx+864y^{2}$$

Combine 288xy and 432yx to get 720xy.

$$4x^{2}+20xy+24y^{2}+144x^{2}+720xy+864y^{2}$$

Combine 4x^{2} and 144x^{2} to get 148x^{2}.

$$148x^{2}+20xy+24y^{2}+720xy+864y^{2}$$

Combine 20xy and 720xy to get 740xy.

$$148x^{2}+740xy+24y^{2}+864y^{2}$$

Combine 24y^{2} and 864y^{2} to get 888y^{2}.

$$148x^{2}+740xy+888y^{2}$$