Question

match each factored form to its standard form. drag & drop the answer 4x² + 25 4x² - 25 4x² + 20x + 25 4x² - 20x + 25 (2x - 5)² (2x + 5)(2x - 5) (2x + 5)²

Explanation:

Step1: Expand \((2x - 5)^2\) using \((a - b)^2=a^{2}-2ab + b^{2}\)

\((2x - 5)^2=(2x)^{2}-2\times(2x)\times5 + 5^{2}=4x^{2}-20x + 25\)

Step2: Expand \((2x + 5)(2x - 5)\) using \((a + b)(a - b)=a^{2}-b^{2}\)

\((2x + 5)(2x - 5)=(2x)^{2}-5^{2}=4x^{2}-25\)

Step3: Expand \((2x + 5)^2\) using \((a + b)^2=a^{2}+2ab + b^{2}\)

\((2x + 5)^2=(2x)^{2}+2\times(2x)\times5+5^{2}=4x^{2}+20x + 25\)

Step4: Match the results

\(4x^{2}+25\) has no match among the factored - forms.
\(4x^{2}-25\) matches \((2x + 5)(2x - 5)\).
\(4x^{2}+20x + 25\) matches \((2x + 5)^2\).
\(4x^{2}-20x + 25\) matches \((2x - 5)^2\).

Answer:

\(4x^{2}+25\) - No match
\(4x^{2}-25\) - \((2x + 5)(2x - 5)\)
\(4x^{2}+20x + 25\) - \((2x + 5)^2\)
\(4x^{2}-20x + 25\) - \((2x - 5)^2\)