Question Video: Distributing a Monomial over a Binomial | Nagwa Question Video: Distributing a Monomial over a Binomial | Nagwa

Question Video: Distributing a Monomial over a Binomial Mathematics • First Year of Preparatory School

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Expand −2𝑥²(𝑥⁴ + 𝑥²).

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Video Transcript

Expand negative two 𝑥 squared times 𝑥 to the fourth power plus 𝑥 squared.

In this question, we are asked to expand a given algebraic expression. To do this, we can note that the given expression is a product of a single term with an expression with two terms. We can expand this expression by recalling the distributive property of multiplication over addition, which tells us 𝑎 times 𝑏 plus 𝑐 is equal to 𝑎𝑏 plus 𝑎𝑐. To apply this to the given expression, we can set 𝑎 equal to negative two 𝑥 squared, 𝑏 equal to 𝑥 to the fourth power, and 𝑐 equal to 𝑥 squared.

However, it is often easier to think of the distribution process as just multiplying every term inside the parentheses by the factor outside. This gives us negative two 𝑥 squared times 𝑥 to the fourth power plus negative two 𝑥 squared multiplied by 𝑥 squared. We can simplify this expression by recalling that multiplication is associative, so we can evaluate the product in any order. We can then use the product rule for exponents, which we recall tells us that 𝑥 to the power of 𝑛 times 𝑥 to the power of 𝑚 equals 𝑥 to the power of 𝑛 plus 𝑚.

Applying this to each term separately gives us negative two 𝑥 to the power of two plus four minus two 𝑥 to the power of two plus two. Evaluating the sum in each exponent then gives us negative two 𝑥 to the sixth power minus two 𝑥 to the fourth power, which is our final answer.

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