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4 years ago

What is the product of (x + 3)(2x – 1)

Mathematics

2 answers:

grigory [225]4 years ago

8 0

Umm
(X+3)(2x-1)
=2x square -x + 6x - 3
=2x square +5x -3

Archy [21]4 years ago

3 0

Answer:

The product of $(x + 3)(2x -1)=2x^2+5x-3$

Step-by-step explanation:

Given : Two expressions (x + 3) and (2x – 1)

We have to find the product of given expression that is $(x + 3)(2x -1)$

Consider the given expression $(x + 3)(2x -1)$

Multiply each term of first bracket with each term of second bracket

$\left(a+b\right)\left(c+d\right)=ac+ad+bc+bd$

we have,

$=x\cdot \:2x+x\left(-1\right)+3\cdot \:2x+3\left(-1\right)$

Simplify, $-(-a)=+a$

we have $=2xx-1\cdot \:x+3\cdot \:2x-3\cdot \:1$

Simplify, we get,

$=2x^2-x+6x-3$

Adding like terms, we have,

$=2x^2+5x-3$

Thus, the product of $(x + 3)(2x -1)=2x^2+5x-3$

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How can i prove this property to be true for all values of n, using mathematical induction.

chubhunter [2.5K]

Proof -

So, in the first part we'll verify by taking n = 1.

$\implies \: 1 = {1}^{2} = \frac{1(1 + 1)(2 + 1)}{6}$

$\implies{ \frac{1(2)(3)}{6} }$

$\implies{ 1}$

Therefore, it is true for the first part.

In the second part we will assume that,

$\: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} = \frac{k(k + 1)(2k + 1)}{6} }$

and we will prove that,

$\sf{ \: { {1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 1 + 1) \{2(k + 1) + 1\}}{6}}}$

$\: {{1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k + 1)(k + 2) (2k + 3)}{6}}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k (k + 1) (2k + 1) }{6} + \frac{(k + 1) ^{2} }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{k(k+1)(2k+1)+6(k+1)^ 2 }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)\{k(2k+1)+6(k+1)\} }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2 +k+6k+6) }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(2k^2+7k+6) }{6}$

${1}^{2} + {2}^{2} + {3}^{2} + ..... + {k}^{2} + (k + 1)^{2} = \frac{(k+1)(k+2)(2k+3) }{6}$

Henceforth, by using the principle of mathematical induction 1²+2² +3²+....+n² = n(n+1)(2n+1)/ 6 for all positive integers n.

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8 0

2 years ago

What is 5 times 82 plus 48

IgorC [24]

Answer:

458

Step-by-step explanation:

5*82= 410

410+48=458

3 0

4 years ago

Read 2 more answers

The area of the pool is 150feet the pool is 5ft deep what is the volume

Vlad [161]

Answer:

750 cubic (^3) feet

Step-by-step explanation:

6 0

4 years ago

A footbridge is in the shape of an arc of a circle. the bridge is 10 ft tall and 27 ft long, horizontally. what is the radius of

lilavasa [31]

See the picture attached to better understand the problem

we know that
the bridge is 10 ft tall and 27 ft long, horizontally
so
BC=10 ft
DE=27 ft---------> DC=27/2----> 13.5 ft
DA=r (radius of the circle)
AC=r-10

Applying the Pythagoras Theorem
DA²=DC²+AC² ------> r²=13.5²+(r-10)²----> r²=182.25+r²-20r+100
20r=282.25--------> r=14.11 ft

the answer is
r=14.11 ft

4 0

4 years ago

The greatest common factor of 4a(2) b and 6ab(3)

Yuliya22 [10]

4a^2b and 6ab^3

first, find the greatest common factor of ur coefficients 4 and 6.....and that is gonna be 2

as for ur variables and exponents....take the lowest ones

so both have an " a " and a " b " variable....the lowest a term is just " a "...and the lowest " b " term is b

so the GCF of these 2 terms are : 2ab

6 0

4 years ago