Solve -left(4x+7right)^2+9left(8+3xright)^2

$$- { \left(4x+7 \right) }^{ 2 } +9 { \left( 8+3x \right) }^{ 2 }$$

Evaluate

$$\left(5x+17\right)\left(13x+31\right)$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4x+7\right)^{2}.

$$-\left(16x^{2}+56x+49\right)+9\left(8+3x\right)^{2}$$

To find the opposite of 16x^{2}+56x+49, find the opposite of each term.

$$-16x^{2}-56x-49+9\left(8+3x\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(8+3x\right)^{2}.

$$-16x^{2}-56x-49+9\left(64+48x+9x^{2}\right)$$

Use the distributive property to multiply 9 by 64+48x+9x^{2}.

$$-16x^{2}-56x-49+576+432x+81x^{2}$$

Add -49 and 576 to get 527.

$$-16x^{2}-56x+527+432x+81x^{2}$$

Combine -56x and 432x to get 376x.

$$-16x^{2}+376x+527+81x^{2}$$

Combine -16x^{2} and 81x^{2} to get 65x^{2}.

$$65x^{2}+376x+527$$

Expand

$$65x^{2}+376x+527$$

Solution Steps

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(4x+7\right)^{2}.

$$-\left(16x^{2}+56x+49\right)+9\left(8+3x\right)^{2}$$

To find the opposite of 16x^{2}+56x+49, find the opposite of each term.

$$-16x^{2}-56x-49+9\left(8+3x\right)^{2}$$

Use binomial theorem \left(a+b\right)^{2}=a^{2}+2ab+b^{2} to expand \left(8+3x\right)^{2}.

$$-16x^{2}-56x-49+9\left(64+48x+9x^{2}\right)$$

Use the distributive property to multiply 9 by 64+48x+9x^{2}.

$$-16x^{2}-56x-49+576+432x+81x^{2}$$

Add -49 and 576 to get 527.

$$-16x^{2}-56x+527+432x+81x^{2}$$

Combine -56x and 432x to get 376x.

$$-16x^{2}+376x+527+81x^{2}$$

Combine -16x^{2} and 81x^{2} to get 65x^{2}.

$$65x^{2}+376x+527$$