Video: Adding Two Algebraic Expressions

Find 𝐴 + 𝐡, given that 𝐴 = 7𝑦² βˆ’ 4𝑦 + 5 and 𝐡 = 3𝑦² βˆ’ 4𝑦 + 1.

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Video Transcript

Find 𝐴 plus 𝐡, given that 𝐴 is equal to seven 𝑦 squared minus four 𝑦 plus five and 𝐡 is equal to three 𝑦 squared minus four 𝑦 plus one.

In order to answer this question, we need to add the two expressions: seven 𝑦 squared minus four 𝑦 plus five plus three 𝑦 squared minus four 𝑦 plus one. We will do this by collecting the like terms: firstly, seven 𝑦 squared plus three 𝑦 squared. Seven plus three is equal to 10. Therefore, seven 𝑦 squared plus three 𝑦 squared is equal to 10𝑦 squared.

Next, we can group or collect the 𝑦 terms: negative four 𝑦 plus negative four 𝑦. Negative four 𝑦 plus negative four 𝑦 is equal to negative eight 𝑦. When we have two signs touching and one is a positive and one is a negative, they turn into a negative sign. We’re therefore left with negative four 𝑦 minus four 𝑦. And negative four minus four equals negative eight.

Finally, we need to group or collect the numbers: plus five plus plus one. Here, the two positives stay positive or an addition sign. Plus five plus one is equal to six. This means that our simplified expression is 10𝑦 squared minus eight 𝑦 plus six.

If 𝐴 is equal to seven 𝑦 squared minus four 𝑦 plus five and 𝐡 is equal to three 𝑦 squared minus four 𝑦 plus one, then 𝐴 plus 𝐡 equals 10𝑦 squared minus eight 𝑦 plus six.

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