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2 years ago

Help!

Mathematics

1 answer:

lord [1]2 years ago

6 0

Answer:

Step-by-step explanation:

The square of the value in the empty space is the constant in the expanded expression. That is ...

[ ]² = 1

The value in the space is ...

[ ] = √1 = 1

The filled-in equation is ...

(3x -1)² = 9x² -6x +1

_____

The expansion of the square of a binomial is ...

(ax -b)² = a²x² -2abx +b²

Above, we used the constant term to find 'b', but we could also have used the linear term:

-6x = -2(3)bx . . . . . a=3 in this problem

1 = b . . . . . . . divide by -6x

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Factor 16x^2 + 49. Check your work.

Shtirlitz [24]

Answer:

$16x^2+49=(x-\frac{7i}{4})(x+\frac{7i}{4})$

Step-by-step explanation:

Given : Expression $16x^2+49$

To find : Factor the expression ?

Solution :

The given expression is a quadratic function $y=ax^2+bx+c$ the solution is $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

On comparing with general form,

a=16, b=0, c=49

Substitute in the formula,

$x=\frac{-0\pm\sqrt{0^2-4(16)(49)}}{2(16)}$

$x=\frac{\pm\sqrt{-3136}}{32}$

$x=\frac{\pm56i}{32}$

$x=\frac{56i}{32},\frac{-56i}{32}$

$x=\frac{7i}{4},\frac{-7i}{4}$

Factors are $(x-\frac{7i}{4}),(x+\frac{7i}{4})$

Therefore, $16x^2+49=(x-\frac{7i}{4})(x+\frac{7i}{4})$

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