Question

Expand.

Your answer should be a polynomial in standard form.
(
x
+
4
)
(
x
+
6
)
=
(x+4)(x+6)=left parenthesis, x, plus, 4, right parenthesis, left parenthesis, x, plus, 6, right parenthesis, equals

Answer 1

Given:-

• A algebraic expression (x+4)(x+6)

To find:-

• To write it in standard form of a polynomial.

Answer:-

We need to write (x+4)(x+6) as a polynomial in standard form. As we know that the standard form of a polynomial is ,

`\implies p(x)= a_n x_n + a_(n-1)x^(n-1) + a_(n-2) x^(n-2) \dots \\`

where ,

• 
  `a_n , a_(n-1) , a_(n-2)\dots` are constants.

So we can expand the given expression as ,

`\implies (x+4)(x+6)\\`

`\implies x(x+6)+4(x+6) \\`

`\implies x^2 + 6x + 4x + 24 \\`

`\implies \underline{\underline{x^2+10x + 24}}\\`

This is the polynomial in standard form.

and we are done!

Answer 2

The standard form of the polynomial is x² + 10x + 24.

Explanation:

To write (x + 4)(x + 6) in standard form, use the FOIL method to expand the brackets.

What is the FOIL method?

FOIL is an acronym that refers to the order of multiplying the terms inside the parentheses of two binomials. Multiply the First terms, then the Outside terms, then the Inside terms, then the Last terms.

(a + b)(c + d) = ac + ad + bc + bd

Therefore:

`\begin{aligned}(x + 4)(x + 6)&=x \cdot x + x \cdot 6 + 4 \cdot x + 4 \cdot 6\\&=x^2+6x+4x+24\\&=x^2+10x+24\end{aligned}`