Question

m⁴+8m²+16=0 factorize
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Answer 1

Mark as BRAINLIEST answer

Answer:

Step by step solution :

Step 1 :

Equation at the end of step 1 :

((m4) + 23m2) + 16 = 0

Step 2 :

Trying to factor by splitting the middle term

2.1 Factoring m4+8m2+16

The first term is, m4 its coefficient is 1 .

The middle term is, +8m2 its coefficient is 8 .

The last term, "the constant", is +16

Step-1 : Multiply the coefficient of the first term by the constant 1 • 16 = 16

Step-2 : Find two factors of 16 whose sum equals the coefficient of the middle term, which is 8 .

-16 + -1 = -17

-8 + -2 = -10

-4 + -4 = -8

-2 + -8 = -10

-1 + -16 = -17

1 + 16 = 17

2 + 8 = 10

4 + 4 = 8 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 4 and 4

m4 + 4m2 + 4m2 + 16

Step-4 : Add up the first 2 terms, pulling out like factors :

m2 • (m2+4)

Add up the last 2 terms, pulling out common factors :

4 • (m2+4)

Step-5 : Add up the four terms of step 4 :

(m2+4) • (m2+4)

Which is the desired factorization

Answer 2

hey mate

here is your answer

${m}^{</em></strong><strong><em>4</em></strong><strong><em>} + </em></strong><strong><em>{</em></strong><strong><em>8m</em></strong><strong><em>}</em></strong><strong><em>^</em></strong><strong><em>{</em></strong><strong><em>2</em></strong><strong><em>}</em></strong><strong><em> + 16 = 0 \\ {m}^{</em></strong><strong><em>4</em></strong><strong><em>} +</em></strong><strong><em>{</em></strong><strong><em> 4m</em></strong><strong><em>}</em></strong><strong><em>^</em></strong><strong><em>{</em></strong><strong><em>2</em></strong><strong><em>}</em></strong><strong><em> +</em></strong><strong><em>{</em></strong><strong><em>4 m </em></strong><strong><em>}</em></strong><strong><em>^</em></strong><strong><em>{</em></strong><strong><em>2</em></strong><strong><em>}</em></strong><strong><em>+ 16 = 0 \\ </em></strong><strong><em>{</em></strong><strong><em>m</em></strong><strong><em>}</em></strong><strong><em>^</em></strong><strong><em>{</em></strong><strong><em>2</em></strong><strong><em>}</em></strong><strong><em>(</em></strong><strong><em>{</em></strong><strong><em>m </em></strong><strong><em>}</em></strong><strong><em>^</em></strong><strong><em>{</em></strong><strong><em>2</em></strong><strong><em>}</em></strong><strong><em>+ 4) + 4(</em></strong><strong><em>{</em></strong><strong><em>m</em></strong><strong><em>}</em></strong><strong><em>^</em></strong><strong><em>{</em></strong><strong><em>2</em></strong><strong><em>}</em></strong><strong><em> + 4) = 0 \\ {(</em></strong><strong><em>{</em></strong><strong><em>m</em></strong><strong><em>}</em></strong><strong><em>^</em></strong><strong><em>{</em></strong><strong><em>2</em></strong><strong><em>}</em></strong><strong><em> + 4)}^{2} </em></strong><strong><em>$

hope it helps u