Solve 81(x+1)^2+90(x+1)(y+2)

$$81 ( x + 1 ) ^ { 2 } + 90 ( x + 1 ) ( y + 2 )$$

Evaluate

$$9\left(x+1\right)\left(9x+10y+29\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$81\left(x^{2}+2x+1\right)+90\left(x+1\right)\left(y+2\right)$$

Use the distributive property to multiply 81 by x^{2}+2x+1.

$$81x^{2}+162x+81+90\left(x+1\right)\left(y+2\right)$$

Use the distributive property to multiply 90 by x+1.

$$81x^{2}+162x+81+\left(90x+90\right)\left(y+2\right)$$

Use the distributive property to multiply 90x+90 by y+2.

$$81x^{2}+162x+81+90xy+180x+90y+180$$

Combine 162x and 180x to get 342x.

$$81x^{2}+342x+81+90xy+90y+180$$

Add 81 and 180 to get 261.

$$81x^{2}+342x+261+90xy+90y$$

Expand

$$81x^{2}+90xy+342x+90y+261$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(x+1\right)^{2}.

$$81\left(x^{2}+2x+1\right)+90\left(x+1\right)\left(y+2\right)$$

Use the distributive property to multiply 81 by x^{2}+2x+1.

$$81x^{2}+162x+81+90\left(x+1\right)\left(y+2\right)$$

Use the distributive property to multiply 90 by x+1.

$$81x^{2}+162x+81+\left(90x+90\right)\left(y+2\right)$$

Use the distributive property to multiply 90x+90 by y+2.

$$81x^{2}+162x+81+90xy+180x+90y+180$$

Combine 162x and 180x to get 342x.

$$81x^{2}+342x+81+90xy+90y+180$$

Add 81 and 180 to get 261.

$$81x^{2}+342x+261+90xy+90y$$