We Distribute, Yet Things Multiply Class 8 Short Question Answer

We Distribute, Yet Things Multiply Class 8 Short Question Answer

We Distribute, Yet Things Multiply Class 8 Short Question Answer

Question 1.

Find the product 97 × 103 using an identity.

Solution:

97 × 103 = (100 - 3) (100 + 3)

= 100² - 3² = 10000 - 9

= 9991.

Question 2.

Find the value of 102², using an identity.

Solution:

102² = (100 + 2)²

= 100² + 2 × 100 × 2 + 2²

= 10000 + 400 + 4

= 10404.

Question 3.

Find the value of 78², using an identity.

Solution:

78² = (80 - 2)² = 80² - 2 × 80 × 2 + 2²

= 6400 - 320 + 4 = 6084.

Question 4.

Find the product of

(x + y + z) (x + y - z).

Solution:

(x + y + z) (x + y - z)

= (x + y)² - z²

[Using (a -b) (a + b) = a² - b²]

= x² + y² + 2xy - z².

Or

(x + y + z) (x + y - z)

= x(x + y - z) + y(x + y - z) + z(x + y - z)

= x² + xy -xz + xy + y² - yz + zx + yz - z²

= x² + y² - z² + 2xy.

Question 5.

Find (7m - 8n)² + (7m + 8n)².

Solution:

(7m - 8n)² + (7m + 8n)²

= 49m² - 2 × 7m × 8n + 64n² + 49m² + 2 × 7m × 8n + 64n²

= 2 × 49m² + 2 × 64n²

= 98m² + 128n².