Solve (3a+5x)(-3a-4x+5)+(2x+a)(3x-4a)=

$$( 3 a + 5 x ) ( - 3 a - 4 x + 5 ) + ( 2 x + a ) ( 3 x - 4 a ) =$$

Evaluate

$$15a-13a^{2}+25x-32ax-14x^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 3a+5x by each term of -3a-4x+5.

$$-9a^{2}-12ax+15a-15xa-20x^{2}+25x+\left(2x+a\right)\left(3x-4a\right)$$

Combine -12ax and -15xa to get -27ax.

$$-9a^{2}-27ax+15a-20x^{2}+25x+\left(2x+a\right)\left(3x-4a\right)$$

Apply the distributive property by multiplying each term of 2x+a by each term of 3x-4a.

$$-9a^{2}-27ax+15a-20x^{2}+25x+6x^{2}-8xa+3ax-4a^{2}$$

Combine -8xa and 3ax to get -5xa.

$$-9a^{2}-27ax+15a-20x^{2}+25x+6x^{2}-5xa-4a^{2}$$

Combine -20x^{2} and 6x^{2} to get -14x^{2}.

$$-9a^{2}-27ax+15a-14x^{2}+25x-5xa-4a^{2}$$

Combine -27ax and -5xa to get -32ax.

$$-9a^{2}-32ax+15a-14x^{2}+25x-4a^{2}$$

Combine -9a^{2} and -4a^{2} to get -13a^{2}.

$$-13a^{2}-32ax+15a-14x^{2}+25x$$

Expand

$$15a-13a^{2}+25x-32ax-14x^{2}$$

Solution Steps

Apply the distributive property by multiplying each term of 3a+5x by each term of -3a-4x+5.

$$-9a^{2}-12ax+15a-15xa-20x^{2}+25x+\left(2x+a\right)\left(3x-4a\right)$$

Combine -12ax and -15xa to get -27ax.

$$-9a^{2}-27ax+15a-20x^{2}+25x+\left(2x+a\right)\left(3x-4a\right)$$

Apply the distributive property by multiplying each term of 2x+a by each term of 3x-4a.

$$-9a^{2}-27ax+15a-20x^{2}+25x+6x^{2}-8xa+3ax-4a^{2}$$

Combine -8xa and 3ax to get -5xa.

$$-9a^{2}-27ax+15a-20x^{2}+25x+6x^{2}-5xa-4a^{2}$$

Combine -20x^{2} and 6x^{2} to get -14x^{2}.

$$-9a^{2}-27ax+15a-14x^{2}+25x-5xa-4a^{2}$$

Combine -27ax and -5xa to get -32ax.

$$-9a^{2}-32ax+15a-14x^{2}+25x-4a^{2}$$

Combine -9a^{2} and -4a^{2} to get -13a^{2}.

$$-13a^{2}-32ax+15a-14x^{2}+25x$$