Factor completely.4m2+20m+254m^2+20m+25

( 2 m + 5 ) 2 \left(2m+5\right)^2 ( 2 m + 5 ) 2

Factor completely. 4 m 2 + 20 m + 25 4m^2+20m+25

Here we want to factor this trinomial completely. Four ms squared plus 20 ms plus 25. So first let's check if this is a perfectly square trinomial. Is four ms squared a perfect square? Yes, because it has the factors two ms times two ms. And is 25 a perfect square? Yes, because it has the factors five and five. So that means I can rewrite these terms as two ms squared and five squared. Now we need to check for our middle term. Does 20 ms equal two times a, which is two ms, times b, which is five. Yes, because two times two is four and four times five is 20. So that means four ms squared plus 20 ms plus 25 can be factored as two ms all squared plus two times two ms times five plus five squared. And since this second term is positive, this can now be factored as two ms plus five all squared.

Factor completely. 4 m 2 + 20 m + 25 4m^2+20m+25

( 2 m + 5 ) 2 \left(2m+5\right)^2 ( 2 m + 5 ) 2

( 4 m + 5 ) 2 \left(4m+5\right)^2

( 2 m + 5 ) ( m + 1 ) \left(2m+5\right)\left(m+1\right) ( 2 m + 5 ) ( m + 1 )

( 4 m + 5 ) ( m + 5 ) \left(4m+5\right)\left(m+5\right) ( 4 m + 5 ) ( m + 5 )

7. Factoring

Factoring Special Products

Beginning Algebra

7. Factoring

Factoring Special Products

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Multiple Choice

Factor completely.
$4 m^{2} + 20 m + 25$

$open paren 4 m plus 5 close paren squared$

$$\left$(2m+5$\right$)^2$

$$\left$(2m+5$\right$)$\left$(m+1$\right$)$

$$\left$(4m+5$\right$)$\left$(m+5$\right$)$

Verified step by step guidance

Identify the general form of a perfect square trinomial, which is either $a^{2} + 2ab + b^{2}$ or $a^{2} - 2ab + b^{2}$.

Look at the given trinomial and check if the first and last terms are perfect squares. For example, check if the first term is a perfect square like $a^{2}$ and the last term is a perfect square like $b^{2}$.

Check the middle term to see if it matches \$2ab$ or $-2ab$, where $a$ and $b$ are the square roots of the first and last terms respectively.

If the trinomial fits the pattern, factor it as $(a + b)^{2}$ if the middle term is positive, or $(a - b)^{2}$ if the middle term is negative.

Write the factored form clearly and verify by expanding it back to ensure it matches the original trinomial.

1:15m

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