All categories

4 years ago

How to simplify this expression??

Mathematics

2 answers:

sdas [7]4 years ago

8 0

Answer :

Step-by-step-explanation :

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

${x}^{2} + 4x + 5 - {x}^{2} - 4x - 4 = {x}^{2} - {x}^{2} + 4x - 4x + 5 - 4 = 5 - 4 = 1$

Mars2501 [29]4 years ago

3 0

Answer:

(x+1) • (x-5)

Step-by-step explanation:

The first term is, x2 its coefficient is 1 .

The middle term is, -4x its coefficient is -4 .

The last term, "the constant", is -5

Step-1 : Multiply the coefficient of the first term by the constant 1 • -5 = -5

Step-2 : Find two factors of -5 whose sum equals the coefficient of the middle term, which is -4 .

-5 + 1 = -4 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 1

x2 - 5x + 1x - 5

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

x • (x-5)

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

1 • (x-5)

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

(x+1) • (x-5)

You might be interested in

9y + 10 = -8 Please explain how you got your answer

Ronch [10]

You are trying to solve for y (get y by itself)

9y + 10 = -8 Subtract 10 on both sides

9y + 10 - 10 = -8 - 10

9y = -18 Divide 9 on both sides

y = -2

8 0

3 years ago

Add or Subtract. (−2^2 − 4 + 13) + (12^2 + 2 − 25) (7^2 + 4 − 26) − (−7^2 − 3 + 15)

aleksklad [387]

Here is your answer

1. (−2^2 − 4 + 13) + (12^2 + 2 − 25)

= (4-4+13)+ (144+2-25)

[Note:- -2^2=(-2×-2)= +4]

= 13+ (146-25)

=13+121

= 134

2. (7^2 + 4 − 26) − (−7^2 − 3 + 15)

= (49+4-26) - (49-3+15)

= 49 +4 -26 -49 +3 -15

= 7-41

= -34

HOPE IT IS USEFUL

6 0

3 years ago

NEED HELP!!!

AnnyKZ [126]

Answer:

see explanation

Step-by-step explanation:

(1)

$\frac{6}{2}$ = $\frac{4}{p}$ ( cross- multiply )

6p = 8 ( divide both sides by 6 )

p = $\frac{8}{6}$ = $\frac{4}{3}$

(2)

$\frac{n}{4}$ = $\frac{8}{7}$ ( cross- multiply )

7n = 32 ( divide both sides by 7 )

n = $\frac{32}{7}$

(3)

$\frac{5}{3}$ = $\frac{x}{4}$ ( cross- multiply )

3x = 20 ( divide both sides by 3 )

x = $\frac{20}{3}$

6 0

3 years ago

The common denominator of 3/4 and 1/6 is 24. True False

Viktor [21]

Actually, this is false. 6 and 4 both have 12 in common because 6*2=12 and 4*3 is 12. So the least common denominator is really 12.

6 0

4 years ago

Tan^2 A/1+cot^2 A + cot^2 A/1+tan^2 A=sec^2 A cosec^2 A-3

omeli [17]

$\frac{tan^2x}{1+cot^2x}+\frac{cot^2x}{1+tan^2x}=sec^2x\ cosec^2x-3\\\\L=\frac{tan^2x(1+tan^2x)+cot^2x(1+cot^2x)}{(1+cot^2x)(1+tan^2x)}=\frac{tan^2x+tan^4x+cot^2x+cot^4x}{1+tan^2x+cot^2x+tanxcotx}\\\\=\frac{tan^2x+cot^2x+tan^4x+cot^4x}{1+tan^2x+cot^2x+1}=\frac{tan^2x+2+cot^2x+tan^4x-2+cot^4x}{tan^2x+cot^2x+2}$

$=\frac{(tanx+cotx)^2+(tan^2x-cot^2x)^2}{(tanx+cotx)^2}=\frac{(tanx+cotx)^2}{(tanx+cotx)^2}+\frac{(tan^2x-cot^2x)^2}{(tanx+cotx)^2}\\\\=1+\frac{(tanx-cotx)^2(tanx+cotx)^2}{(tanx+cotx)^2}=1+(tanx-cotx)^2\\\\=1+tan^2x-2tanx\ cotx+cot^2x=tan^2x+cot^2x+1-2\\\\=\left(\frac{sinx}{cosx}\right)^2+\left(\frac{cosx}{sinx}\right)^2-1=\frac{sin^2x}{cos^2x}+\frac{cos^2x}{sin^2x}-1=\frac{sin^4x+cos^4x}{sin^2x\ cos^2x}-1$

$=\frac{(sin^2x)^2+2sin^2x\ cos^2x+(cos^2x)^2-2sin^2x\ cos^2x}{sin^2x\ cos^2x}-1\\\\=\frac{(sin^2x+cos^2x)^2-2sin^2x\ cos^2x}{sin^2x\ cos^2x}-1=\frac{1^2-2sin^2x\ cos^2x}{sin^2x\ cos^2x}-1\\\\=\frac{1}{sin^2x\ cos^2x}-\frac{2sin^2x\ cos^2x}{sin^2x\ cos^2x}-1=\frac{1}{sin^2x}\cdot\frac{1}{cos^2x}-2-1\\\\=cosec^2x\cdot sec^2x-3=sec^2x\ cosec^2x-3=R$

3 0

4 years ago