Find the product of the following(i) (5x + 3) (2x + 4)
The correct answer and explanation is:
To find the product of the two binomials (5x+3)(2x+4)(5x + 3)(2x + 4), we can use the distributive property, also known as the FOIL method (First, Outer, Inner, Last). Here’s how to expand the expression step-by-step: (5x+3)(2x+4)(5x + 3)(2x + 4)
- First: Multiply the first terms in each binomial: 5x×2x=10x25x \times 2x = 10x^2
- Outer: Multiply the outer terms: 5x×4=20x5x \times 4 = 20x
- Inner: Multiply the inner terms: 3×2x=6×3 \times 2x = 6x
- Last: Multiply the last terms in each binomial: 3×4=123 \times 4 = 12
Now, combine all these terms: 10×2+20x+6x+1210x^2 + 20x + 6x + 12
Next, combine like terms (the two terms with xx): 10×2+(20x+6x)+12=10×2+26x+1210x^2 + (20x + 6x) + 12 = 10x^2 + 26x + 12
Thus, the product of (5x+3)(2x+4)(5x + 3)(2x + 4) is: 10×2+26x+1210x^2 + 26x + 12
Explanation:
The distributive property is fundamental to multiplying polynomials. By applying the FOIL method, you ensure that every term in the first binomial multiplies with every term in the second binomial. The key idea is to carefully distribute each term, making sure that no combination is missed. This method simplifies the process of multiplying binomials and is applicable to any similar expressions involving the multiplication of two binomials.
In this case, the result consists of three terms: a quadratic term, a linear term, and a constant term. Each term is derived from the individual products of the terms in the binomials, and combining like terms gives the final simplified expression.