Video: Using Distributive Property to Find the Value of an Unknown in an Algebraic Equation

Given that 16π‘Žβ΅π‘Β² + 26π‘Ž = 2π‘Ž(8π‘Žβ΄π‘Β² + π‘˜) what is the value of π‘˜?

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Video Transcript

Given that 16π‘Ž to the power of five 𝑏 squared plus 26π‘Ž is equal to two π‘Ž multiplied by eight π‘Ž to the power of four 𝑏 squared plus π‘˜, what is the value of π‘˜?

In order to answer this question, we need to factorize the equation by taking out the highest common factor. In this case, the highest common factor is two π‘Ž. This is because two is the highest common factor of 16 and 26. And π‘Ž is the only other term in both parts of the equation.

Dividing 16π‘Ž to the power of five 𝑏 squared by two π‘Ž gives us eight π‘Ž to the power of four 𝑏 squared as 16 divided by two is equal to eight and π‘Ž to the power of five divided by π‘Ž is equal to π‘Ž to the power of four. This means that the first term inside our parentheses is eight π‘Ž to the power of four 𝑏 squared.

Dividing the second term 26π‘Ž by two π‘Ž gives us an answer of 13 as 26 divided by two is 13 and π‘Ž divided by π‘Ž is one. 13 multiplied by one is equal to 13. This means that the second term inside the parentheses is 13 plus 13.

As 13 is in the same position as the π‘˜ in the question, we can say that π‘˜ is equal to 13. We can check this answer by multiplying our two π‘Ž outside the parentheses by the 13 inside the parentheses, which gives us 26π‘Ž, the term that we started with.

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