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Problem 13 Easy Difficulty

Perform the indicated operations.
$$\left(\frac{2}{5} y+\frac{1}{8} z\right)\left(\frac{3}{5} y+\frac{1}{2} z\right)$$

Answer

$\therefore\left(\frac{2}{5} y+\frac{1}{8} z\right)\left(\frac{3}{5} y+\frac{1}{2} z\right)=\frac{6}{25} y^{2}+\frac{11}{40} y z+\frac{1}{16} z^{2}$

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Video Transcript

{'transcript': "we're being asked to foil the quantity to wide of the fifth plus five z, meaning we need to take too wide of the fifth. That's terrible too high to the fifth plus five z, and we need to multiply it by itself another too wide of the fifth plus five z making this affording problem. Or if you notice that this works for a special product formula, you could use that to I'm just gonna foil it out first. Two terms to White of the fifth times to White of the fifth, two times two is four. Why did the fifth times wider the fifth? When we multiply like basis, we add the exponents of five plus five would give us why to the 10th outer two terms too wide of the fifth times five z two times five is 10. Why did the fifth Z is just gonna be rewritten? Because those aren't like variables, so we can't combine them into one thing. In her two terms five z times to white of the fifth, five times two is 10 again and again, we have a wide of the fifth Z noticed that those air in alphabetical order still last two terms five z times five z five times five is 25 z times E Izzy Squared Last step is simply to combine are like terms in the middle. So I rewrite the four y to the 10th 10 wide of the fifth Z plus 10 wide of the fifth Z would give us 20. Why to the fifth Z 10 plus tennis 20. And then we'd end with rewriting that 25 z squared. That would be our final answer."}