algebraic expressions with like terms.

Notice how the distributive property is used to combine 6x and 2x.

6x + 2x = (6 + 2)x = 8x

The distributive property can also be used to add and subtract expressions containing radicals.

$$3\sqrt{2} + 7 \sqrt{2} = (3 + 7)\sqrt{2} = 10 \sqrt{2}$$

$$We \ call \ 3\sqrt{2}\ and \ 7 \sqrt{2} \ like\ radicals$$

$$a. \ 3\sqrt{2} + 2 \sqrt{3}$$
$$b. \ 8\sqrt{3} + 5 \sqrt{3}$$

a. has the same index, but the radicand is not the same.

b. has the same radicand, but the index is not the same.

$$6\sqrt{5} + 3 \sqrt{5} = (6 + 3)\sqrt{5} = 9 \sqrt{5}$$

$$18\sqrt{7} - 5 \sqrt{7}- \sqrt{7} = (18 - 5 - 1)\sqrt{7}$$
$$18\sqrt{7} - 5 \sqrt{7} - \sqrt{7} = 12\sqrt{7}$$

Sometimes, you may need to simplify each radical until you get the same radicand before you add and / or subtract radicals. The next example demonstrates how.

$$\sqrt{50} + \sqrt{8} = \sqrt{25 \times 2} + \sqrt{4 \times 2}$$
$$\sqrt{50} + \sqrt{8} = \sqrt{25} \times \sqrt{ 2} + \sqrt{4} \times \sqrt{2}$$
$$\sqrt{50} + \sqrt{8} = 5\sqrt{ 2} + 2\sqrt{2}$$
$$\sqrt{50} + \sqrt{8} = (5 + 2) \sqrt{ 2}$$
$$\sqrt{50} + \sqrt{8} = 7 \sqrt{ 2}$$

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