Question

$(y + 2)(y - 3)(y + 8)(y + 3) + 56$
solve it please
​

Answer 1

Answer:

y(y+3)+2(y+3)y(y+8)−3(y+8)+56

(y {}^{2} + 3y + 2y + 6) \: (y {}^{2} + 8y - 3y - 24) + 56(y

2

+3y+2y+6)(y

2

+8y−3y−24)+56

(y {}^{2} + 5y + 6) \: (y { }^{2} + 5y - 24) + 56(y

2

+5y+6)(y

2

+5y−24)+56

y {}^{2} + 5y = x \: takingy

2

+5y=xtaking

\begin{gathered}(x + 6) \: (x - 24) + 56 \\ \\ x(x - 24) + 6(x - 24) + 56 \\ \\ x {}^{2} - 24x + 6x - 144 + 56 \\ \\ x {}^{2} - 18x - 144 + 56 \\ \\ x {}^{2} - 18x - 88 \\ \\ x {}^{2} - 22x - 4x - 88 \\ \\ x(x - 22) + 4(x - 22) \\ \\ (x - 22) \: (x + 4) \\ \\ \\ substituting \: the \: value \: of \: x \: with \: y {}^{2} + 5y \\ \\ \\ (y {}^{2} + 5y - 22) \: (y {}^{2} + 5y + 4) \\ \\ (y {}^{2} + 5y - 22) \: (y {}^{2} + 4y + y + 4) \\ \\ (y {}^{2} - 5y - 22) \: {y(y + 4) + 1(y + 4)} \\ \\ (y {}^{2} - 5y - 22) \: (y + 4) \: (y + 1) \: \: are \: the \: solution \: \end{gathered}

(x+6)(x−24)+56

x(x−24)+6(x−24)+56

x

2

−24x+6x−144+56

x

2

−18x−144+56

x

2

−18x−88

x

2

−22x−4x−88

x(x−22)+4(x−22)

(x−22)(x+4)

substitutingthevalueofxwithy

2

+5y

(y

2

+5y−22)(y

2

+5y+4)

(y

2

+5y−22)(y

2

+4y+y+4)

(y

2

−5y−22)y(y+4)+1(y+4)

(y

2

−5y−22)(y+4)(y+1)arethesolution

Answer 2

Step-by-step explanation:

Solution :-

Given that

(y + 2)(y - 3)(y + 8)(y + 3) + 56

=> [(y + 2)(y +3)][(y + 8)(y - 3)] + 56

=> [y(y+3)+2(y+3)][y(y-3)+8(y-3)]+56

=> (y²+3y+2y+6)(y²-3y+8y-24)+56

=> (y²+5y+6)(y²+5y-24)+56

Put y²+5y = a then

=> (a+6)(a-24)+56

=> a(a-24)+6(a-24)+56

=> a²-24a+6a-144+56

=> a²-18a-88

=> a²+4a-22a-88

=> a(a+4)-22(a+4)

=> (a+4)(a-22)

=> (y²+5a+4)(y²+5a-22)

=> (y²+a+4a+4)(y²+5a-22)

=>[y(y+1)+4(a+1)](y²+5a-22)

=> (y+1)(y+4)(y²+5a-22)

Answer:-

(y + 2)(y - 3)(y + 8)(y + 3) + 56 =

(y+1)(y+4)(y²+5a-22)

Used formulae:-

→ Splitting the middle term