Solve (a+5b)(5a-b)=5a^2-ab+25ab-5b^2=

$$( a + 5 b ) ( 5 a - b ) = 5 a ^ { 2 } - a b + 25 a b - 5 b ^ { 2 } =$$

Solve for a (complex solution)

$$a\in \mathrm{C}$$

Solution Steps

Use the distributive property to multiply a+5b by 5a-b and combine like terms.

$$5a^{2}+24ab-5b^{2}=5a^{2}-ab+25ab-5b^{2}$$

Combine -ab and 25ab to get 24ab.

$$5a^{2}+24ab-5b^{2}=5a^{2}+24ab-5b^{2}$$

Subtract 5a^{2} from both sides.

$$5a^{2}+24ab-5b^{2}-5a^{2}=24ab-5b^{2}$$

Combine 5a^{2} and -5a^{2} to get 0.

$$24ab-5b^{2}=24ab-5b^{2}$$

Subtract 24ab from both sides.

$$24ab-5b^{2}-24ab=-5b^{2}$$

Combine 24ab and -24ab to get 0.

$$-5b^{2}=-5b^{2}$$

Cancel out -5 on both sides.

$$b^{2}=b^{2}$$

Reorder the terms.

$$\text{true}$$

This is true for any a.

$$a\in \mathrm{C}$$

Solve for b (complex solution)

$$b\in \mathrm{C}$$

Solution Steps

Use the distributive property to multiply a+5b by 5a-b and combine like terms.

$$5a^{2}+24ab-5b^{2}=5a^{2}-ab+25ab-5b^{2}$$

Combine -ab and 25ab to get 24ab.

$$5a^{2}+24ab-5b^{2}=5a^{2}+24ab-5b^{2}$$

Subtract 24ab from both sides.

$$5a^{2}+24ab-5b^{2}-24ab=5a^{2}-5b^{2}$$

Combine 24ab and -24ab to get 0.

$$5a^{2}-5b^{2}=5a^{2}-5b^{2}$$

Add 5b^{2} to both sides.

$$5a^{2}-5b^{2}+5b^{2}=5a^{2}$$

Combine -5b^{2} and 5b^{2} to get 0.

$$5a^{2}=5a^{2}$$

Cancel out 5 on both sides.

$$a^{2}=a^{2}$$

Reorder the terms.

$$\text{true}$$

This is true for any b.

$$b\in \mathrm{C}$$

Solve for a

$$a\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply a+5b by 5a-b and combine like terms.

$$5a^{2}+24ab-5b^{2}=5a^{2}-ab+25ab-5b^{2}$$

Combine -ab and 25ab to get 24ab.

$$5a^{2}+24ab-5b^{2}=5a^{2}+24ab-5b^{2}$$

Subtract 5a^{2} from both sides.

$$5a^{2}+24ab-5b^{2}-5a^{2}=24ab-5b^{2}$$

Combine 5a^{2} and -5a^{2} to get 0.

$$24ab-5b^{2}=24ab-5b^{2}$$

Subtract 24ab from both sides.

$$24ab-5b^{2}-24ab=-5b^{2}$$

Combine 24ab and -24ab to get 0.

$$-5b^{2}=-5b^{2}$$

Cancel out -5 on both sides.

$$b^{2}=b^{2}$$

Reorder the terms.

$$\text{true}$$

This is true for any a.

$$a\in \mathrm{R}$$

Solve for b

$$b\in \mathrm{R}$$

Solution Steps

Use the distributive property to multiply a+5b by 5a-b and combine like terms.

$$5a^{2}+24ab-5b^{2}=5a^{2}-ab+25ab-5b^{2}$$

Combine -ab and 25ab to get 24ab.

$$5a^{2}+24ab-5b^{2}=5a^{2}+24ab-5b^{2}$$

Subtract 24ab from both sides.

$$5a^{2}+24ab-5b^{2}-24ab=5a^{2}-5b^{2}$$

Combine 24ab and -24ab to get 0.

$$5a^{2}-5b^{2}=5a^{2}-5b^{2}$$

Add 5b^{2} to both sides.

$$5a^{2}-5b^{2}+5b^{2}=5a^{2}$$

Combine -5b^{2} and 5b^{2} to get 0.

$$5a^{2}=5a^{2}$$

Cancel out 5 on both sides.

$$a^{2}=a^{2}$$

Reorder the terms.

$$\text{true}$$

This is true for any b.

$$b\in \mathrm{R}$$