Multiply the polynomials (4x^2+4x+6)(7x+5)

28x^3 +48x^2 +62x +30

Step-by-step explanation:

You can use the distributive property to identify the separate terms, then combine terms:

... = 7x(4x^2 +4x +6) +5(4x^2 +4x +6)

... = 28x^3 +28x^2 +42x + 20x^2 +20x +30

... = 28x^3 +x^2(28+20) +x(42 +20) +30

... = 28x^3 +48x^2 +62x +30

___

Or, you can recognize where the product terms come from, and combine terms as you go. This can be done in your head as you write down the answer.

... The x^3 term comes from 7x·4x^2 = 28x^3

... The x^2 term comse from 7x·4x +5·4x^2 = 28x^2 +20x^2 = 48x^2

... The x term comes from 7x·6 +5·4x = 42x +20x = 62x

... The constant term comes from 5·6 = 30

So, you can write down the result as 28x^3 +48x^2 +62x +30.

solution:

→c= a b , that is product of a and b is possible only when when a is m × n matrix and b is n × p matrix.

that is, number of columns of a= number of rows of b.

so, size of matrix , c= a b is , if a = (m × n)matrix

b= (n × p)matrix

then a b = [ (m × n)matrix] ×[   (n × p)matrix ]

→→c= a b= [m × p ] matrix

→→size of product a b will be equal to = number of rows of a × number of columns of b