Question Video: Expanding Two Linear Brackets | Nagwa Question Video: Expanding Two Linear Brackets | Nagwa

# Question Video: Expanding Two Linear Brackets Mathematics • First Year of Preparatory School

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Expand the product (π₯ + 4)(π₯ + 6).

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### Video Transcript

Expand the product π₯ plus four multiplied by π₯ plus six.

Here, weβre asked to expand the product of two algebraic expressions, π₯ plus four and π₯ plus six. In fact, these expressions are both binomials because they each contain two terms. When multiplying two binomials together, we must make sure we multiply each term in the first binomial by each term in the second, which will give four terms overall, before we perform any simplification.

We can do this in a number of ways. One way is to use the grid method. We can picture the product of these two expressions as a rectangle with side lengths of π₯ plus four and π₯ plus six units. The product of these expressions corresponds to the area of the rectangle, which we divide into four smaller rectangles.

We can find the area of each of these rectangles by multiplying their length by their width. For the top-left rectangle, π₯ multiplied by π₯ gives π₯ squared. Then, for the bottom-left rectangle, π₯ multiplied by six is six π₯. The final two rectangles have areas of four π₯ and 24 square units. Summing these four expressions gives an expression for the total area of the larger rectangle and, hence, an expression for the given product. Finally, collecting like terms gives that the product of π₯ plus four and π₯ plus six is equal to π₯ squared plus 10π₯ plus 24.

An alternative method is just to use a systematic approach to ensure we multiply each term in the first binomial by each term in the second. If we multiply the first terms in each binomial together, we obtain π₯ squared. Then, if we multiply the terms on the outside of the product together, we obtain six π₯. Multiplying the terms on the inside of the product together gives four π₯. And finally multiplying the last term in each binomial together gives 24.

We obtained four terms as expected, and then we can simplify by grouping the like terms. Weβve found that the expanded and simplified form of the product π₯ plus four multiplied by π₯ plus six is π₯ squared plus 10π₯ plus 24.

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