बेरीज करा: 3y² - 10y + 16 ; 2y - 7
Answers
Step by step solution :
Step 1 :
16 Simplify —— 3
Equation at the end of step 1 :
16 ((((3•(y2))+8y)-(——•y2))+10y)-8 3
Step 2 :
Equation at the end of step 2 :
16y2 ((((3•(y2))+8y)-————)+10y)-8 3
Step 3 :
Equation at the end of step 3 :
16y2 (((3y2 + 8y) - ————) + 10y) - 8 3
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 3 as the denominator :
3y2 + 8y (3y2 + 8y) • 3 3y2 + 8y = ———————— = —————————————— 1 3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
3y2 + 8y = y • (3y + 8)
Adding fractions that have a common denominator :
5.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
y • (3y+8) • 3 - (16y2) 24y - 7y2 ——————————————————————— = ————————— 3 3
Equation at the end of step 5 :
(24y - 7y2) (——————————— + 10y) - 8 3
Step 6 :
Rewriting the whole as an Equivalent Fraction :
6.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 3 as the denominator :
10y 10y • 3 10y = ——— = ——————— 1 3
Step 7 :
Pulling out like terms :
7.1 Pull out like factors :
24y - 7y2 = -y • (7y - 24)
Adding fractions that have a common denominator :
7.2 Adding up the two equivalent fractions
-y • (7y-24) + 10y • 3 54y - 7y2 —————————————————————— = ————————— 3 3
Equation at the end of step 7 :
(54y - 7y2) ——————————— - 8 3
Step 8 :
Rewriting the whole as an Equivalent Fraction :
8.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 3 as the denominator :
8 8 • 3 8 = — = ————— 1 3
Step 9 :
Pulling out like terms :
9.1 Pull out like factors :
54y - 7y2 = -y • (7y - 54)
Adding fractions that have a common denominator :
9.2 Adding up the two equivalent fractions
-y • (7y-54) - (8 • 3) -7y2 + 54y - 24 —————————————————————— = ——————————————— 3 3
Step 10 :
Pulling out like terms :
10.1 Pull out like factors :
-7y2 + 54y - 24 = -1 • (7y2 - 54y + 24)
Trying to factor by splitting the middle term
10.2 Factoring 7y2 - 54y + 24
The first term is, 7y2 its coefficient is 7 .
The middle term is, -54y its coefficient is -54 .
The last term, "the constant", is +24
Step-1 : Multiply the coefficient of the first term by the constant 7 • 24 = 168
Step-2 : Find two factors of 168 whose sum equals the coefficient of the middle term, which is -54 .
-168 + -1 = -169 -84 + -2 = -86 -56 + -3 = -59 -42 + -4 = -46 -28 + -6 = -34 -24 + -7 = -31
For tidiness, printing of 26 lines which failed to find two such factors, was suppressed
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
-7y2 + 54y - 24 / 3
Step by step solution :
Step 1 :
16 Simplify —— 3
Equation at the end of step 1 :
16 ((((3•(y2))+8y)-(——•y2))+10y)-8 3
Step 2 :
Equation at the end of step 2 :
16y2 ((((3•(y2))+8y)-————)+10y)-8 3
Step 3 :
Equation at the end of step 3 :
16y2 (((3y2 + 8y) - ————) + 10y) - 8 3
Step 4 :
Rewriting the whole as an Equivalent Fraction :
4.1 Subtracting a fraction from a whole
Rewrite the whole as a fraction using 3 as the denominator :
3y2 + 8y (3y2 + 8y) • 3 3y2 + 8y = ———————— = —————————————— 1 3
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator
Step 5 :
Pulling out like terms :
5.1 Pull out like factors :
3y2 + 8y = y • (3y + 8)
Adding fractions that have a common denominator :
5.2 Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
y • (3y+8) • 3 - (16y2) 24y - 7y2 ——————————————————————— = ————————— 3 3
Equation at the end of step 5 :
(24y - 7y2) (——————————— + 10y) - 8 3
Step 6 :
Rewriting the whole as an Equivalent Fraction :
6.1 Adding a whole to a fraction
Rewrite the whole as a fraction using 3 as the denominator :
10y 10y • 3 10y = ——— = ——————— 1 3
Step 7 :
Pulling out like terms :
7.1 Pull out like factors :
24y - 7y2 = -y • (7y - 24)
Adding fractions that have a common denominator :
7.2 Adding up the two equivalent fractions
-y • (7y-24) + 10y • 3 54y - 7y2 —————————————————————— = ————————— 3 3
Equation at the end of step 7 :
(54y - 7y2) ——————————— - 8 3
Step 8 :
Rewriting the whole as an Equivalent Fraction :
8.1 Subtracting a whole from a fraction
Rewrite the whole as a fraction using 3 as the denominator :
8 8 • 3 8 = — = ————— 1 3
Step 9 :
Pulling out like terms :
9.1 Pull out like factors :
54y - 7y2 = -y • (7y - 54)
Adding fractions that have a common denominator :
9.2 Adding up the two equivalent fractions
-y • (7y-54) - (8 • 3) -7y2 + 54y - 24 —————————————————————— = ——————————————— 3 3
Step 10 :
Pulling out like terms :
10.1 Pull out like factors :
-7y2 + 54y - 24 = -1 • (7y2 - 54y + 24)
Trying to factor by splitting the middle term
10.2 Factoring 7y2 - 54y + 24
The first term is, 7y2 its coefficient is 7 .
The middle term is, -54y its coefficient is -54 .
The last term, "the constant", is +24
Step-1 : Multiply the coefficient of the first term by the constant 7 • 24 = 168
Step-2 : Find two factors of 168 whose sum equals the coefficient of the middle term, which is -54 .
-168 + -1 = -169 -84 + -2 = -86 -56 + -3 = -59 -42 + -4 = -46 -28 + -6 = -34 -24 + -7 = -31
For tidiness, printing of 26 lines which failed to find two such factors, was suppressed
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
Final result :
-7y2 + 54y - 24