[tex]\large\huge\green{\sf{Question:-}}[/tex]
- Find the product of following
- (4v-7)(4v+7)
- (1+3p)(1-3p)
- (a+5)²
- (2w+5)³
- (3m-2)³
- (2x-3)(x²-4x+4)
[tex]\large\huge\green{\sf{Answer:-}}[/tex]
[tex](1).(4v-7)(4v+7) \\ formula : - \\ (a - b)(a + b) = (a {}^{2} - b {}^{2} ) \\ therefore.. \\ (4v-7)(4v+7) = \\ (4v) {}^{2} - (7) {}^{2} \\ 16v {}^{2} - 49[/tex]
..
[tex](2). \: (1+3p)(1-3p) \\ \:formula : - \\ (a + b)(a - b) = (a {}^{2} - b {}^{2} ) \\ therefore..(1) {}^{2} - (3p) {}^{2} \\ = 1 - 9p {}^{2} [/tex]
...
[tex](3)..(a+5) {}^{2} \\ formua : - \\ (a + b) {}^{2} = a {}^{2} + 2ab + b {}^{2} \\ (a+5) {}^{2} = {a}^{2} +( 2 \times a \times 5) + 5 { }^{2} \\ (a+5) {}^{2} = {a}^{2} + 10a + 25[/tex]
(4.)
[tex](2w+5)³ \\ formula :- \\ (a+b) {}^{3} =a3+3a {}^{2} b+3ab {}^{2} +b {}^{3} . \\ = (2) {}^{3} + 3 \times (2w) {}^{2} \times 5 + 3 \times 2w \times (5) {}^{2} + (5) {}^{3} \\ = 8 + 60w {}^{2} + 150w + 125[/tex]
(5).
(3m-2)³
= (3m)³-(2)³-[ 3x (3m)² x (2) ]+ [ 3x (3m) x (2)²] -(2)³
= 27m³- 8 - 84m²+36m -8
formula Used :-
(a - b)³ = a³ - 3a²b + 3ab²- b³
(6)
(2x-3)(x²-4x+4)
=2x(x²-4x+4) -3(x²-4x+4)
=2x³-8x²+8x -3x²+12x -12
=2x³-11x²+20x -12
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[tex]\large\huge\green{\sf{Question:-}}[/tex]
☆ -DIRECTIONS:- Read and understand the problem carefully then solve.Show your complete solutions.
- . If the length of the Rubik's cube measures (3x+1) cm, what is its volume in terms of x?
[tex]\large\huge\green{\sf{Given:-}}[/tex]
- the length of the Rubik's cube measures (3x+1) cm
[tex]\large\huge\green{\sf{ToFind:-}}[/tex]
- Volume of cube in terms of x= ??
[tex]\large\huge\green{\sf{FormulaRequired:-}}[/tex]
- volume of cube= (side)³
- (a + b)³ = a³ + 3a²b + 3ab²+ b³
[tex]\large\huge\green{\sf{Solution:-}}[/tex]
- the length of the Rubik's cube measures (3x+1) cm
- Volume of cube = (side)³
- Volume of cube = (3x+1)³
we know
(a + b)³ = a³ + 3a²b + 3ab²+ b³
:- (3x+1)³= (3x)³+ [ 3 x (3x)² x (1) ]
+ [ 3 x (3x) x (1)²] +(1)³
= 27x³+ 27x²+ 9x +1
☆
