Video: Multiplying Two Algebraic Expressions

Find 𝐴𝐡 given 𝐴 = 5π‘₯Β³ βˆ’ 3π‘₯ and 𝐡 = βˆ’6π‘₯Β² + 3π‘₯.

02:47

Video Transcript

Find 𝐴𝐡 given 𝐴 equals five π‘₯ cubed minus three π‘₯ and 𝐡 equals negative six π‘₯ squared plus three π‘₯.

𝐴𝐡 would be multiplying the expression of 𝐴 and the expression of 𝐡. We need to multiply five π‘₯ cubed minus three π‘₯ times negative six π‘₯ squared plus three π‘₯. We do that by foiling. Multiplying the firsts, the outers, the inners, and the lasts. The first, five π‘₯ cubed times negative six π‘₯ squared. And then, five π‘₯ cubed times three π‘₯. So we’ll add five π‘₯ cubed times three π‘₯.

We need to be careful here. We’re multiplying negative three π‘₯ by negative six π‘₯ squared. That means we’ll be adding negative three π‘₯ times negative six π‘₯ squared and then negative three π‘₯ times positive three π‘₯. So we’ll add negative three π‘₯ times positive three π‘₯. Five times negative six equals negative 30. We bring down the variable and then add the two exponents. Three plus two is five. Five π‘₯ cubed times negative six π‘₯ squared equals negative 30π‘₯ to the fifth.

Follow the same procedure. Multiply the coefficients. Five times three equals 15. Bring down the π‘₯. Three π‘₯ is the same thing as three times π‘₯ to the first power. And three plus one is four. Five π‘₯ cubed times three π‘₯ equals 15π‘₯ to the fourth.

The next term, we’ll multiply negative three times negative six, which is positive 18. And then, we’ll add the exponents of the two π‘₯s. One plus two is three. The last term has negative three times positive three, which is negative nine. Both of these π‘₯-values have an exponent of one. π‘₯ times π‘₯ is the same thing as π‘₯ to the one plus one power. It’s π‘₯ squared.

We’re adding all these terms together, negative 30π‘₯ to the fifth plus 15π‘₯ to the fourth plus 18π‘₯ cubed. For the last term, we’re adding a negative. And we can simplify that by saying subtracting nine π‘₯ squared.

𝐴𝐡 equals negative 30π‘₯ to the fifth plus 15π‘₯ to the fourth plus 18π‘₯ cubed minus nine π‘₯ squared.

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