Question

Write an equivalent expression in standard form for
(5x + 4)(7x+ -12x + 27).

Answer 1

Answer: -25x² + 115x + 108

Concept:

When encountering questions that ask for simplifying polynomial expressions, using the method FOIL would be easier:

• First, which means multiplying the first terms together;
• Outer, which means that we multiply the outermost terms when the binomials are placed side by side;
• Inner, which means multiply the innermost terms together;
• Last, which means multiplying the last term in each binomial together;

Solve:

Given

(5x + 4) (7x + (-12x) + 27)

Combine like terms in the parentheses

=(5x + 4) (7x - 12x + 27)

=(5x + 4) (-5x + 27)

Expand parentheses and apply the FOIL method

=-25x² + 135x - 20x + 108

Combine like terms

=
`\boxed {-25x^2+115x+108}`

Hope this helps!! :)

Please let me know if you have any questions

Answer 2

`\boxed {\boxed {\sf -25x^2+115x+108}}`

Explanation:

We are asked to find an equivalent expression for (5x + 4)(7x+ -12x + 27). Note that we are multiplying 2 polynomials.

`(5x + 4)(7x+ -12x + 27)`

Notice that the second polynomial has like terms. There are 2 terms with an x (7x and -12x) and we can combine them.

`(5x + 4)[(7x+ -12x) + 27]`

`(5x + 4)[(-5x) + 27]`

`(5x+4)(-5x+27)`

Now we are multiplying 2 binomials. Therefore, we use the FOIL method. We multiply the First terms, the Outside terms, the Inside terms, and the Last terms.

• First: 5x * -5x = -25x²
• Outside: 5x * 27 = 135x
• Inside: 4* -5x = -20x
• Last: 4 * 27=108

`-25x^2+135x-20x+108`

Notice there are 2 terms with an x ( 135x and -20x). They are like terms and can be combined.

`-25x^2+(135x-20x)+108`

`-25x^2+115x+108`

The equivalent expression in standard form is -25x²+115x+108