expand the following by algrbraic Indities
Answers
(3y+4z)³ = 27y³ + 64z³ + 108y²z+144yz²
(3x³+7y³) = 27x³+353y³
79³-56³ =317,423
Explanation:
Given:
1. (3y+4z)³
2. (3x³+7y³)
3. 79³-56³
Formula:
(a+b)³ =a³+b³+3ab(a+b)
(a-b)³ = a³-b³-3ab(a-b)
a³+b³ =(a+b)(a²+b²-ab)
a³-b³ =(a-b)(a²+b²+ab)
1. (3y+4z)³
Expand:
a = 3y
b = 4z
Substitute in the formula
==> (a+b)³ =a³+b³+3ab(a+b)
==> (3y+4z)³ = (3y)³ + (4z)³ + 3(3y)(4z)(3y+4z)
==> (3y+4z)³ = 27y³ + 64z³ + (9y)(4z)(3y+4z)
==> (3y+4z)³ = 27y³ + 64z³ + (36yz)(3y+4z)
==> (3y+4z)³ = 27y³ + 64z³ + 108y²z+144yz²
2. (3x³+7y³)
Expand:
a = 3x
b = 7y
Substitute in the formula
==> a³+b³ =(a+b)(a²+b²-ab)
==> (3x³+7y³) = (3x+7y)((3x)²+(7y)²-(3x)(7y))
==> (3x³+7y³) = (3x+7y)(9x²+49y²-21xy)
==> (3x³+7y³) = (3x)(9x²+49y²-21xy)+7y(9x²+49y²-21xy)
==> (3x³+7y³) = (27x³+147xy²-63x²y)+ (63x²y+353y³-147xy²)
==> (3x³+7y³) = 27x³+353y³+147xy²-147xy²-63x²y+ 63x²y
==> +147xy²-147xy² gets cancel
==> -63x²y+ 63x²y gets cancel
==> (3x³+7y³) = 27x³+353y³
3. 79³-56³
Expand:
a = 79
b = 56
Substitute in the formula
==> a³-b³ =(a-b)(a²+b²+ab)
==> 79³-56³ = (79-56)(79²+56²+(79)(56))
==> 79³-56³ = (23)(6241+3136 +4424)
==> 79³-56³ = (23)(13801)
==> 79³-56³ =317,423